A000560 Number of ways of folding a strip of n labeled stamps. (Formerly M1420 N0557)

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

2,2

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.

Sequence in context: A010843 A084075 A209717 * A292212 A212823 A292213

Adjacent sequences: A000557 A000558 A000559 * A000561 A000562 A000563

Keyword

nonn,nice

Author

N. J. A. Sloane, Stéphane Legendre

Extensions

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

Status

approved