A000682 -id:A000682 - cp's OEIS frontend

A000136 Number of ways of folding a strip of n labeled stamps.

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

Offset: 1

N. J. A. Sloane

nonn

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.

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]
Thomas C. Hull, Adham Ibrahim, Jacob Paltrowitz, Natalya Ter-Saakov, and Grace Wang, The Stamp Folding Problem From a Mountain-Valley Perspective: Enumerations and Bounds, arXiv:2503.23661 [math.CO], 2025. See p. 1.
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
Bowie Liu, Dennis Wong, Chan-Tong Lam, and Marcus Im, Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meanders, arXiv:2411.05458 [cs.DS], 2024. See p. 2.
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 and 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

Cf. A000560, A000682.

a(n) = 2*n * A000560(n-1) for n >= 3.

a(n) = n * A000682(n). - Andrew Howroyd, Dec 06 2015

A000560 Number of ways of folding a strip of n labeled stamps.

Original entry on oeis.org

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

Offset: 2

N. J. A. Sloane, Stéphane Legendre

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.

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

Cf. A000136, A000682, A001011.

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 *)

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)

Computed to n = 45 by Iwan Jensen - see link in A000682.

A060206 Number of rotationally symmetric closed meanders of length 4n+2.

Original entry on oeis.org

1, 2, 10, 66, 504, 4210, 37378, 346846, 3328188, 32786630, 329903058, 3377919260, 35095839848, 369192702554, 3925446804750, 42126805350798, 455792943581400, 4967158911871358, 54480174340453578, 600994488311709056, 6664356253639465480

Offset: 0

N. J. A. Sloane, Apr 10 2001

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.

R. Bacher, Meander algebras
Andrew Howroyd, Illustration of a(1) and a(2)

Cf. A000682, A005315, A077055, A077460, A223096.

Meander sequences in Bacher's paper: A060066, A060089, A060111, A060148, A060149, A060174, A060198.

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 *)

a(n) = A000682(2n + 1). - Andrew Howroyd, Nov 24 2015

Name edited by Andrew Howroyd, Nov 24 2015

a(7)-a(20) from Andrew Howroyd, Nov 24 2015

A001011 Number of ways to fold a strip of n blank stamps.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Stéphane Legendre

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).

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

Cf. A000682, A086441.

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 *)

a(n) = (A001010(n) + A000136(n)) / 4 for n >= 2. - Andrew Howroyd, Dec 07 2015

a(17) and a(20) corrected by Sean A. Irvine, Mar 17 2013

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).

Original entry on oeis.org

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

Offset: 2

N. J. A. Sloane, Jul 04 2015

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

			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;
  ...

A. Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949.

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]

Row sums give A000682.

Column k=2 is A260785.

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

Terms a(22) and beyond from Andrew Howroyd, Dec 05 2018

A046726 Triangle of numbers of semi-meanders of order n with k components.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Rows are in order of decreasing number of components. Diagonals give number of semi-meanders with k components. - Andrew Howroyd, Nov 27 2015

			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;
  ...

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.

Diagonals include A000682, A046721, A046722, A046723, A046724, A046725. Columns include A000027, A046691. Row sums are in A000108 (Catalan numbers).

More terms from Larry Reeves (larryr(AT)acm.org), Apr 05 2000

T(12,k)-T(40,k) from Andrew Howroyd, Dec 07 2015

A077460 Number of nonisomorphic ways a loop can cross a road (running East-West) 2n times.

Original entry on oeis.org

1, 1, 1, 3, 12, 70, 464, 3482, 27779, 233556, 2038484, 18357672, 169599492, 1601270562, 15401735750, 150547249932, 1492451793728, 14980801247673, 152047178479946, 1558569469867824, 16119428039548246

Offset: 0

N. J. A. Sloane and Jon Wild, Dec 03 2002

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

			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

Andrew Howroyd, Illustration of Closed Meander Symmetries

The total number of closed meanders with 2n crossings is given in A005315. Cf. A000682, A005316, A060206, A077055, A078104, A078105, A078591.

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 *)

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)

a(10)-a(20) from Andrew Howroyd, Nov 24 2015

A301620 a(n) is the total number of top arches with exactly one covering arch for semi-meanders with n top arches.

Original entry on oeis.org

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

Offset: 1

Roger Ford, Mar 24 2018

nonn

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

			For n = 4, a(4) = 4.  + + are underneath the starting and ending of each arch with exactly one covering arch.
          /\                  /\
         //\\         /\     //\\       /\
      /\///\\\,  /\/\//\\,  ///\\\/\,  //\\/\/\ .
         +  +         ++     +  +       ++

Jean-François Alcover, Table of n, a(n) for n = 1..43

Cf. A000682, A259689.

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 *)

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

A001010 Number of symmetric foldings of a strip of n stamps.

Original entry on oeis.org

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, 332523306, 65573260, 1130110294, 205022836, 3846372944, 659806116, 13109737832, 2084555444, 44735866296, 6755838520

Offset: 1

N. J. A. Sloane, Stéphane Legendre

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).

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

Cf. A007822, A000682.

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 *)

a(1) = 1, a(2n-1) = 2*A007822(n), a(2n) = 2*A000682(n+1). - Sean A. Irvine, Mar 18 2013; corrected by Hunter Hogan, Aug 08 2025

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).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Mar 29 2013

nonn

Subset of foldings of n labeled stamps (A000136). - Stéphane Legendre, Apr 09 2013

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

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 *)

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

Name clarified by Stéphane Legendre, Apr 09 2013

More terms from Stéphane Legendre, Apr 09 2013

cp's OEIS Frontend

A000136 Number of ways of folding a strip of n labeled stamps.

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A000560 Number of ways of folding a strip of n labeled stamps.

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A060206 Number of rotationally symmetric closed meanders of length 4n+2.

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Mathematica

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A001011 Number of ways to fold a strip of n blank stamps.

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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).

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A046726 Triangle of numbers of semi-meanders of order n with k components.

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A077460 Number of nonisomorphic ways a loop can cross a road (running East-West) 2n times.

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A301620 a(n) is the total number of top arches with exactly one covering arch for semi-meanders with n top arches.

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