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Search: a000682 -id:a000682
Displaying 1-10 of 34 results found. page 1 2 3 4
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A000136 Number of ways of folding a strip of n labeled stamps.
(Formerly M1614 N0630) 		+10
15
1, 2, 6, 16, 50, 144, 462, 1392, 4536, 14060, 46310, 146376, 485914, 1557892, 5202690, 16861984, 56579196, 184940388, 622945970, 2050228360, 6927964218, 22930109884, 77692142980, 258360586368, 877395996200, 2929432171328, 9968202968958, 33396290888520, 113837957337750 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 238.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..45
Oswin Aichholzer, Florian Lehner, and Christian Lindorfer, Folding polyominoes into cubes, arXiv:2402.14965 [cs.CG], 2024. See p. 9.
T. Asano, E. D. Demaine, M. L. Demaine and R. Uehara, NP-completeness of generalized Kaboozle, J. Information Processing, 20 (July, 2012), 713-718.
CombOS - Combinatorial Object Server, Generate meanders and stamp foldings
R. Dickau, Stamp Folding
R. Dickau, Stamp Folding [Cached copy, pdf format, with permission]
J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152.
J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152. [Annotated, corrected, scanned copy]
Stéphane Legendre, The 16 foldings of 4 labeled stamps
W. F. Lunnon, A map-folding problem, Math. Comp. 22 (1968), 193-199.
David Orden, In how many ways can you fold a strip of stamps?, 2014.
A. Panayotopoulos, P. Vlamos, Partitioning the Meandering Curves, Mathematics in Computer Science (2015) p 1-10.
Frank Ruskey, Information on Stamp Foldings
M. A. Sainte-Laguë, Les Réseaux (ou Graphes), Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1923, 64 pages. See p. 41.
M. A. Sainte-Laguë, Les Réseaux (ou Graphes), Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1923, 64 pages. See p. 41. [Incomplete annotated scan of title page and pages 18-51]
J. Sawada and R. Li, Stamp foldings, semi-meanders, and open meanders: fast generation algorithms, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).
Eric Weisstein's World of Mathematics, Stamp Folding
M. B. Wells, Elements of Combinatorial Computing, Pergamon, Oxford, 1971. [Annotated scanned copy of pages 237-240]
Index entries for sequences obtained by enumerating foldings
FORMULA
a(n) = n * A000682(n). - Andrew Howroyd, Dec 06 2015
CROSSREFS
Equals 2n*A000560 (and so 45 terms are known).
KEYWORD
nonn
AUTHOR
N. J. A. Sloane
STATUS
approved
A060206 Number of rotationally symmetric closed meanders of length 4n+2. +10
10
1, 2, 10, 66, 504, 4210, 37378, 346846, 3328188, 32786630, 329903058, 3377919260, 35095839848, 369192702554, 3925446804750, 42126805350798, 455792943581400, 4967158911871358, 54480174340453578, 600994488311709056, 6664356253639465480 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Closed meanders of other lengths do not have rotational symmetry. - Andrew Howroyd, Nov 24 2015
See A077460 for additional information on the symmetries of closed meanders.
LINKS
Table of n, a(n) for n=0..20.
R. Bacher, Meander algebras
Andrew Howroyd, Illustration of a(1) and a(2)
FORMULA
a(n) = A000682(2n + 1). - Andrew Howroyd, Nov 24 2015
MATHEMATICA
A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];
a[n_] := A000682[[2n + 1]];
a /@ Range[0, 20] (* Jean-François Alcover, Sep 03 2019 *)
CROSSREFS
Cf. A000682, A005315, A077055, A077460, A223096.
Meander sequences in Bacher's paper: A060066, A060089, A060111, A060148, A060149, A060174, A060198.
KEYWORD
nonn,nice
AUTHOR
N. J. A. Sloane, Apr 10 2001
EXTENSIONS
Name edited by Andrew Howroyd, Nov 24 2015
a(7)-a(20) from Andrew Howroyd, Nov 24 2015
STATUS
approved
A000560 Number of ways of folding a strip of n labeled stamps.
(Formerly M1420 N0557) 		+10
9
1, 2, 5, 12, 33, 87, 252, 703, 2105, 6099, 18689, 55639, 173423, 526937, 1664094, 5137233, 16393315, 51255709, 164951529, 521138861, 1688959630, 5382512216, 17547919924, 56335234064, 184596351277, 596362337295, 1962723402375 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
REFERENCES
A. Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 238.
LINKS
T. D. Noe, Table of n, a(n) for n = 2..44 (derived from A000682)
CombOS - Combinatorial Object Server, Generate meanders and stamp foldings
P. Di Francesco, O. Golinelli and E. Guitter, Meanders: a direct enumeration approach, arXiv:hep-th/9607039, 1996; Nucl. Phys. B 482 [FS] (1996), 497-535.
R. Dickau, Stamp Folding
R. Dickau, Stamp Folding [Cached copy, pdf format, with permission]
I. Jensen, Home page
I. Jensen, A transfer matrix approach to the enumeration of plane meanders, J. Phys. A 33, 5953-5963 (2000).
I. Jensen and A. J. Guttmann, Critical exponents of plane meanders J. Phys. A 33, L187-L192 (2000).
J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152.
W. F. Lunnon, A map-folding problem, Math. Comp. 22 (1968), 193-199.
David Orden, In how many ways can you fold a strip of stamps?, 2014.
A. Panayotopoulos, P. Vlamos, Partitioning the Meandering Curves, Mathematics in Computer Science (2015) p 1-10.
Albert Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949. [Annotated scanned copy]
J. Sawada and R. Li, Stamp foldings, semi-meanders, and open meanders: fast generation algorithms, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).
J. Touchard, Contributions à l'étude du problème des timbres poste, Canad. J. Math., 2 (1950), 385-398.
M. B. Wells, Elements of Combinatorial Computing, Pergamon, Oxford, 1971. [Annotated scanned copy of pages 237-240]
Index entries for sequences obtained by enumerating foldings
FORMULA
a(n) = (1/2)*A000682(n+1) for n >= 2.
a(n) = A000136(n+1)/(2*n+2) for n >= 2. - Jean-François Alcover, Sep 06 2019 (from formula in A000136)
MATHEMATICA
A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];
a[n_] := A000682[[n + 1]]/2;
a /@ Range[2, 44] (* Jean-François Alcover, Sep 03 2019 *)
A000136 = Import["https://oeis.org/A000136/b000136.txt", "Table"][[All, 2]];
a[n_] := A000136[[n + 1]]/(2 n + 2);
a /@ Range[2, 44] (* Jean-François Alcover, Sep 06 2019 *)
CROSSREFS
Cf. A000136, A000682, A001011.
KEYWORD
nonn,nice
AUTHOR
N. J. A. Sloane, Stéphane Legendre
EXTENSIONS
Computed to n = 45 by Iwan Jensen - see link in A000682.
STATUS
approved
A001011 Number of ways to fold a strip of n blank stamps.
(Formerly M1455 N0576) 		+10
9
1, 1, 2, 5, 14, 38, 120, 353, 1148, 3527, 11622, 36627, 121622, 389560, 1301140, 4215748, 14146335, 46235800, 155741571, 512559195, 1732007938, 5732533570, 19423092113, 64590165281, 219349187968, 732358098471, 2492051377341, 8349072895553, 28459491475593 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
M. Gardner, Mathematical Games, Sci. Amer. Vol. 209 (No. 3, Mar. 1963), p. 262.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence - see entry 576, Fig. 17, and the front cover).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..45 [from S. Legendre, 2013]
B. Bobier and J. Sawada, A fast algorithm to generate open meandric systems and meanders, Transactions on Algorithms, Vol. 6 No. 2 (2010) 12 pages.
S. P. Castell, Computer Puzzles, Computer Bulletin, March 1975, pages 3, 33, 34. [Annotated scanned copy]
CombOS - Combinatorial Object Server, Generate meanders and stamp foldings.
Santo Diano, Letter to N. J. A. Sloane, circa Dec 01 1979.
R. Dickau, Stamp Folding.
R. Dickau, Stamp Folding. [Cached copy, pdf format, with permission]
R. Dickau, Unlabeled Stamp Foldings.
R. Dickau, Unlabeled Stamp Foldings. [Cached copy, pdf format, with permission]
R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152.
J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152. [Annotated, corrected, scanned copy]
S. Legendre, Foldings and Meanders, arXiv preprint arXiv:1302.2025 [math.CO], 2013.
S. Legendre, Foldings and Meanders, Aust. J. Comb. 58(2), 275-291, 2014.
David Orden, In how many ways can you fold a strip of stamps?, 2014.
Frank Ruskey, Information on Stamp Foldings.
J. Sawada and R. Li, Stamp foldings, semi-meanders, and open meanders: fast generation algorithms, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).
N. J. A. Sloane, Illustration of initial terms. (Fig. 17 of the 1973 Handbook of Integer Sequences. The initial terms are also embossed on the front cover.)
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 2.
Eric Weisstein's World of Mathematics, Stamp Folding.
Index entries for sequences obtained by enumerating foldings
FORMULA
a(n) = (A001010(n) + A000136(n)) / 4. - Andrew Howroyd, Dec 07 2015
MATHEMATICA
A000136 = Import["https://oeis.org/A000136/b000136.txt", "Table"][[All, 2]];
A001010 = Cases[Import["https://oeis.org/A001010/b001010.txt", "Table"], {_, _}][[All, 2]];
a[n_] := If[n == 1, 1, (A001010[[n]] + A000136[[n]])/4];
Array[a, 45] (* Jean-François Alcover, Sep 04 2019 *)
CROSSREFS
Cf. A000682, A086441.
KEYWORD
nonn,nice
AUTHOR
N. J. A. Sloane, Stéphane Legendre
EXTENSIONS
a(17) and a(20) corrected by Sean A. Irvine, Mar 17 2013
STATUS
approved
A259689 Irregular triangle read by rows: T(n,k) is the number of degree-n permutations without overlaps which furnish k new permutations without overlaps upon the addition of an (n+1)st element, 2 <= k <= 1 + floor(n/2). +10
8
1, 2, 2, 2, 6, 4, 10, 10, 4, 32, 26, 8, 68, 64, 34, 8, 220, 186, 82, 16, 528, 488, 276, 98, 16, 1724, 1484, 744, 226, 32, 4460, 4086, 2382, 980, 258, 32, 14664, 12752, 6822, 2498, 578, 64, 39908, 36384, 21616, 9576, 3088, 642, 64, 131944, 115508, 64264, 26040, 7552, 1410, 128 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
COMMENTS
See Sade for precise definition.
From Roger Ford, Dec 07 2018: (Start)
T(n,k) is the number of semi-meanders with n top arches, k top arch groupings and a rainbow of bottom arches.
Example: /\ /\
n=4 k=3 //\\ /\ /\, /\ /\ //\\ T(4,3) = 2
.
/\ /\
//\\ //\\
n=4 k=2 ///\\\ /\, /\ ///\\\ T(4,2) = 2. (End)
Stéphane Legendre's solutions for folding a strip of stamps with leaf 1 on top have the same numeric sequences and total solutions as Albert Sade's permutations without overlaps. Stéphane Legendre's "Illustration of initial terms" link in A000682 models the values for Albert Sade's array. - Roger Ford, Dec 24 2018
REFERENCES
A. Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..170
Albert Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949. [Annotated scanned copy]
FORMULA
Sum_{k>=2} k*T(n,k) = A000682(n + 1). - Andrew Howroyd, Dec 07 2018
T(n, floor(n/2)) = 2^floor((n-1)/2)*(n-4)+2. - Roger Ford, Dec 04 2018
For n>2, T(n, floor((n+2)/2)) = 2^(floor((n-1)/2)). - Roger Ford, Aug 18 2023
EXAMPLE
Triangle begins, n >= 2, 2 <= k <= 1 + floor(n/2):
1;
2;
2, 2;
6, 4;
10, 10, 4;
32, 26, 8;
68, 64, 34, 8;
220, 186, 82, 16;
528, 488, 276, 98, 16;
1724, 1484, 744, 226, 32;
4460, 4086, 2382, 980, 258, 32;
...
CROSSREFS
Row sums give A000682.
Column k=2 is A260785.
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jul 04 2015
EXTENSIONS
Terms a(22) and beyond from Andrew Howroyd, Dec 05 2018
STATUS
approved
A046726 Triangle of numbers of semi-meanders of order n with k components. +10
7
1, 1, 1, 1, 2, 2, 1, 3, 6, 4, 1, 4, 11, 16, 10, 1, 5, 17, 37, 48, 24, 1, 6, 24, 66, 126, 140, 66, 1, 7, 32, 104, 254, 430, 428, 174, 1, 8, 41, 152, 438, 956, 1454, 1308, 504, 1, 9, 51, 211, 690, 1796, 3584, 4976, 4072, 1406, 1, 10, 62, 282, 1023, 3028, 7238, 13256, 16880, 12796, 4210 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Rows are in order of decreasing number of components. Diagonals give number of semi-meanders with k components. - Andrew Howroyd, Nov 27 2015
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..820
P. Di Francesco, O. Golinelli, and E. Guitter, Meander, folding and arch statistics, arXiv:hep-th/9506030, 1995.
P. Di Francesco, O. Golinelli, and E. Guitter, Meander, folding and arch statistics, Mathematical and Computer Modelling 26 (1997), 97-147.
EXAMPLE
Triangle starts:
1;
1, 1;
1, 2, 2;
1, 3, 6, 4;
1, 4, 11, 16, 10;
1, 5, 17, 37, 48, 24;
1, 6, 24, 66, 126, 140, 66;
1, 7, 32, 104, 254, 430, 428, 174;
1, 8, 41, 152, 438, 956, 1454, 1308, 504;
...
CROSSREFS
Diagonals include A000682, A046721, A046722, A046723, A046724, A046725. Columns include A000027, A046691. Row sums are in A000108 (Catalan numbers).
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Apr 05 2000
T(12,k)-T(40,k) from Andrew Howroyd, Dec 07 2015
STATUS
approved
A077460 Number of nonisomorphic ways a loop can cross a road (running East-West) 2n times. +10
7
1, 1, 1, 3, 12, 70, 464, 3482, 27779, 233556, 2038484, 18357672, 169599492, 1601270562, 15401735750, 150547249932, 1492451793728, 14980801247673, 152047178479946, 1558569469867824, 16119428039548246 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Nonisomorphic closed meanders, where two closed meanders are considered equivalent if one can be obtained from the other by reflections in an East-West or North-South mirror (a group of order 4).
Symmetries are possible by reflection in a North-South mirror, or by rotation through 180 degrees when n is odd.(see illustration). - Andrew Howroyd, Nov 24 2015
LINKS
Table of n, a(n) for n=0..20.
Andrew Howroyd, Illustration of Closed Meander Symmetries
FORMULA
From Andrew Howroyd, Nov 24 2015: (Start)
a(2n+1) = (A005315(2n+1) + A005316(2n+1) + A060206(n)) / 4.
a(2n) = (A005315(2n) + 2 * A005316(2n)) / 4. (End)
EXAMPLE
A meander can be specified by marking 2n equally spaced points along a line and recording the order in which the meander visits the points.
For n = 2, 4, 6, 8 the solutions are as follows:
n=2: 1 2
n=4: 1 2 3 4
n=6: 1 2 3 4 5 6, 1 2 3 6 5 4, 1 2 5 4 3 6
n=8: 1 2 3 4 5 6 7 8, 1 2 3 4 5 8 7 6, 1 2 3 4 7 6 5 8, 1 2 7 6 3 4 5 8, 1 2 3 6 7 8 5 4, 1 2 3 6 5 4 7 8, 1 2 7 6 5 4 3 8, 1 2 3 8 5 6 7 4, 1 2 3 8 7 4 5 6, 1 2 5 6 7 4 3 8, 1 2 7 4 5 6 3 8, 1 4 3 2 7 6 5 8
MATHEMATICA
A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];
A005316 = Cases[Import["https://oeis.org/A005316/b005316.txt", "Table"], {_, _}][[All, 2]];
a[0] = a[1] = 1;
a[n_] := If[OddQ[n], (A005316[[n + 1]] + A005316[[2n]] + A000682[[n]])/4, (A005316[[2n]] + 2 A005316[[n + 1]])/4];
a /@ Range[0, 20] (* Jean-François Alcover, Sep 06 2019, after Andrew Howroyd *)
CROSSREFS
The total number of closed meanders with 2n crossings is given in A005315. Cf. A000682, A005316, A060206, A077055, A078104, A078105, A078591.
KEYWORD
nonn,nice
AUTHOR
N. J. A. Sloane and Jon Wild, Dec 03 2002
EXTENSIONS
a(10)-a(20) from Andrew Howroyd, Nov 24 2015
STATUS
approved
A301620 a(n) is the total number of top arches with exactly one covering arch for semi-meanders with n top arches. +10
5
0, 0, 2, 4, 18, 42, 156, 398, 1398, 3778, 12982, 36522, 124290, 360182, 1220440, 3618090, 12237698, 36938158, 124880222, 382471606, 1293363816, 4009185912, 13565790984, 42478788432, 143851766298, 454339269482, 1539997455570, 4900091676662, 16624834778474, 53240459608298 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
For n>2, a(n-2) is the number of ways to fold a strip of n stamps with leaf 1 on top and the n leaf not adjacent to the n-1 leaf. Example n = 6, a(6-2) = 4: 125436, 126345, 154362, 163452. - Roger Ford, Mar 29 2019
For n>2, a(n-2) is the number of ways to fold a strip of n stamps with leaf 1 on top and leaf 2 not in the second position and not in the n-th position. Example, for n = 6, a(6-2) = 4: 143265, 156234, 165234, 143256. - Roger Ford, Mar 12 2021
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..43
FORMULA
a(n) = A000682(n+2) - 2*A000682(n+1).
a(n) = Sum_{k=3..floor((n+3)/2)} (A259689(n+1,k)*(k-2)). - Roger Ford, Dec 10 2018
a(n) = 2*A259702(n+2). - Roger Ford, Dec 24 2018
EXAMPLE
For n = 4, a(4) = 4. + + are underneath the starting and ending of each arch with exactly one covering arch.
/\ /\
//\\ /\ //\\ /\
/\///\\\, /\/\//\\, ///\\\/\, //\\/\/\ .
+ + ++ + + ++
MATHEMATICA
A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];
a[n_] := A000682[[n + 2]] - 2*A000682[[n + 1]];
Array[a, 30] (* Jean-François Alcover, Sep 02 2019 *)
CROSSREFS
Cf. A000682, A259689.
KEYWORD
nonn
AUTHOR
Roger Ford, Mar 24 2018
STATUS
approved
A001010 Number of symmetric foldings of a strip of n stamps.
(Formerly M0323 N0120) 		+10
4
1, 2, 2, 4, 6, 8, 18, 20, 56, 48, 178, 132, 574, 348, 1870, 1008, 6144, 2812, 20314, 8420, 67534, 24396, 225472, 74756, 755672, 222556, 2540406, 693692, 8564622, 2107748, 28941258, 6656376, 98011464, 20548932 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..52
R. Dickau, Symmetric Stamp Foldings
R. Dickau, Symmetric Stamp Foldings [Cached copy, pdf format, with permission]
J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152.
J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152. [Annotated, corrected, scanned copy]
Frank Ruskey, Information on Stamp Foldings
Eric Weisstein's World of Mathematics, Stamp Folding.
Index entries for sequences obtained by enumerating foldings
FORMULA
a(2n) = 2*A000682(n+2), a(2n+1) = 2*A007822(n). - Sean A. Irvine, Mar 18 2013
MATHEMATICA
A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];
A007822 = Cases[Import["https://oeis.org/A007822/b007822.txt", "Table"], {_, _}][[All, 2]];
a[n_] := Which[n == 1, 1, EvenQ[n], 2*A000682[[n/2 + 1]], OddQ[n], 2*A007822[[(n - 1)/2 + 1]]];
Array[a, 52] (* Jean-François Alcover, Sep 03 2019, updated Jul 13 2022 *)
CROSSREFS
Cf. A007822, A000682.
KEYWORD
nonn,nice
AUTHOR
N. J. A. Sloane, Stéphane Legendre
STATUS
approved
A223093 Number of foldings of n labeled stamps in which leaf 1 is inwards and leaf n outwards (or leaf 1 outwards and leaf n inwards). +10
3
0, 0, 2, 4, 16, 38, 132, 342, 1144, 3134, 10370, 29526, 97458, 285458, 942920, 2822310, 9341008, 28440970, 94358558, 291294678, 968853072, 3025232480, 10086634316, 31797822936, 106265437078, 337731551446, 1131117792978, 3620119437762, 12148796744234, 39118879440938 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Subset of foldings of n labeled stamps (A000136). - Stéphane Legendre, Apr 09 2013
LINKS
Stéphane Legendre, Table of n, a(n) for n = 1..42
S. Legendre, Foldings and Meanders, arXiv preprint arXiv:1302.2025 [math.CO], 2013.
S. Legendre, Foldings and Meanders, Aust. J. Comb. 58(2), 275-291, 2014.
Index entries for sequences obtained by enumerating foldings
FORMULA
a(n) = A000682(n+1) - A077014(n). - Andrew Howroyd, Dec 06 2015
A217310(n) = 2*a(n) if n is odd and A217310(n) = a(n) if n is even. - Stéphane Legendre, Jan 09 2014
MATHEMATICA
A000682 = Cases[Import["https://oeis.org/A000682/b000682.txt", "Table"], {_, _}][[All, 2]];
A077014 = Cases[Import["https://oeis.org/A077014/b077014.txt", "Table"], {_, _}][[All, 2]];
a[n_] := A000682[[n + 1]] - A077014[[n + 1]];
Array[a, 30] (* Jean-François Alcover, Sep 07 2019, after Andrew Howroyd *)
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 29 2013
EXTENSIONS
Name clarified by Stéphane Legendre, Apr 09 2013
More terms from Stéphane Legendre, Apr 09 2013
STATUS
approved
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Last modified September 6 05:09 EDT 2024. Contains 375703 sequences. (Running on oeis4.)