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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 (list; graph; refs; listen; history; text; internal format)



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)

P. Di Francesco, O. Golinelli and E. Guitter, Meanders: a direct enumeration approach, 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


a(n) = (1/2)*A000682(n+1) for n >= 2.


Cf. A000682, A001011.

Sequence in context: A010843 A084075 A209717 * A292212 A212823 A292213

Adjacent sequences:  A000557 A000558 A000559 * A000561 A000562 A000563




N. J. A. Sloane, Stéphane Legendre


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



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Last modified March 21 16:42 EDT 2018. Contains 301025 sequences. (Running on oeis4.)