A000136 - OEIS

A000136

Number of ways of folding a strip of n labeled stamps.
(Formerly M1614 N0630)

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).

Sequence in context: A151445 A213429 A195645 * A369365 A013989 A002841

Adjacent sequences: A000133 A000134 A000135 * A000137 A000138 A000139

KEYWORD

nonn