cp's OEIS Frontend

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

%I A000136 M1614 N0630 #116 Jul 26 2025 19:59:01
%S A000136 1,2,6,16,50,144,462,1392,4536,14060,46310,146376,485914,1557892,
%T A000136 5202690,16861984,56579196,184940388,622945970,2050228360,6927964218,
%U A000136 22930109884,77692142980,258360586368,877395996200,2929432171328,9968202968958,33396290888520,113837957337750
%N A000136 Number of ways of folding a strip of n labeled stamps.
%D A000136 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000136 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A000136 M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 238.
%H A000136 T. D. Noe, <a href="/A000136/b000136.txt">Table of n, a(n) for n = 1..45</a>
%H A000136 Oswin Aichholzer, Florian Lehner, and Christian Lindorfer, <a href="https://arxiv.org/abs/2402.14965">Folding polyominoes into cubes</a>, arXiv:2402.14965 [cs.CG], 2024. See p. 9.
%H A000136 T. Asano, E. D. Demaine, M. L. Demaine and R. Uehara, <a href="https://dspace.jaist.ac.jp/dspace/bitstream/10119/10710/1/17799.pdf">NP-completeness of generalized Kaboozle</a>, J. Information Processing, 20 (July, 2012), 713-718.
%H A000136 CombOS - Combinatorial Object Server, <a href="http://combos.org/meander">Generate meanders and stamp foldings</a>
%H A000136 R. Dickau, <a href="http://www.robertdickau.com/stampfolding.html">Stamp Folding</a>
%H A000136 R. Dickau, <a href="/A000136/a000136_2.pdf">Stamp Folding</a> [Cached copy, pdf format, with permission]
%H A000136 Thomas C. Hull, Adham Ibrahim, Jacob Paltrowitz, Natalya Ter-Saakov, and Grace Wang, <a href="https://arxiv.org/abs/2503.23661">The Stamp Folding Problem From a Mountain-Valley Perspective: Enumerations and Bounds</a>, arXiv:2503.23661 [math.CO], 2025. See p. 1.
%H A000136 J. E. Koehler, <a href="http://dx.doi.org/10.1016/S0021-9800(68)80048-1">Folding a strip of stamps</a>, J. Combin. Theory, 5 (1968), 135-152.
%H A000136 J. E. Koehler, <a href="/A001011/a001011_4.pdf">Folding a strip of stamps</a>, J. Combin. Theory, 5 (1968), 135-152. [Annotated, corrected, scanned copy]
%H A000136 Stéphane Legendre, <a href="/A000136/a000136_1.pdf">The 16 foldings of 4 labeled stamps</a>
%H A000136 Bowie Liu, Dennis Wong, Chan-Tong Lam, and Marcus Im, <a href="https://arxiv.org/abs/2411.05458">Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meanders</a>, arXiv:2411.05458 [cs.DS], 2024. See p. 2.
%H A000136 W. F. Lunnon, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0221957-8 ">A map-folding problem</a>, Math. Comp. 22 (1968), 193-199.
%H A000136 David Orden, <a href="http://mappingignorance.org/2014/07/07/many-ways-can-fold-strip-stamps/">In how many ways can you fold a strip of stamps?</a>, 2014.
%H A000136 A. Panayotopoulos and P. Vlamos, <a href="http://dx.doi.org/10.1007/s11786-015-0234-0">Partitioning the Meandering Curves</a>, Mathematics in Computer Science (2015) p 1-10.
%H A000136 Frank Ruskey, <a href="http://combos.org/meander">Information on Stamp Foldings</a>
%H A000136 M. A. Sainte-Laguë, <a href="https://eudml.org/doc/192551">Les Réseaux (ou Graphes)</a>, Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1923, 64 pages. See p. 41.
%H A000136 M. A. Sainte-Laguë, <a href="/A002560/a002560.pdf">Les Réseaux (ou Graphes)</a>, 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]
%H A000136 J. Sawada and R. Li, <a href="https://doi.org/10.37236/2404">Stamp foldings, semi-meanders, and open meanders: fast generation algorithms</a>, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).
%H A000136 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StampFolding.html">Stamp Folding</a>
%H A000136 M. B. Wells, <a href="/A000170/a000170.pdf">Elements of Combinatorial Computing</a>, Pergamon, Oxford, 1971. [Annotated scanned copy of pages 237-240]
%H A000136 <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>
%F A000136 a(n) = 2*n * A000560(n-1) for n >= 3.
%F A000136 a(n) = n * A000682(n). - _Andrew Howroyd_, Dec 06 2015
%Y A000136 Cf. A000560, A000682.
%K A000136 nonn
%O A000136 1,2
%A A000136 _N. J. A. Sloane_