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A000136 Number of ways of folding a strip of n labeled stamps.
(Formerly M1614 N0630)
14

%I M1614 N0630

%S 1,2,6,16,50,144,462,1392,4536,14060,46310,146376,485914,1557892,

%T 5202690,16861984,56579196,184940388,622945970,2050228360,6927964218,

%U 22930109884,77692142980,258360586368,877395996200,2929432171328,9968202968958,33396290888520,113837957337750

%N Number of ways of folding a strip of n labeled stamps.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 238.

%H T. D. Noe, <a href="/A000136/b000136.txt">Table of n, a(n) for n = 1..45</a>

%H 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 CombOS - Combinatorial Object Server, <a href="http://combos.org/meander">Generate meanders and stamp foldings</a>

%H R. Dickau, <a href="http://www.robertdickau.com/stampfolding.html">Stamp Folding</a>

%H R. Dickau, <a href="/A000136/a000136_2.pdf">Stamp Folding</a> [Cached copy, pdf format, with permission]

%H 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 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 Stéphane Legendre, <a href="/A000136/a000136_1.pdf">The 16 foldings of 4 labeled stamps</a>

%H 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 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 A. Panayotopoulos, 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 Frank Ruskey, <a href="http://combos.org/meander">Information on Stamp Foldings</a>

%H 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 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 J. Sawada and R. Li, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i2p43">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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StampFolding.html">Stamp Folding</a>

%H M. B. Wells, <a href="/A000170/a000170.pdf">Elements of Combinatorial Computing</a>, Pergamon, Oxford, 1971. [Annotated scanned copy of pages 237-240]

%H <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>

%F a(n) = n * A000682(n). - _Andrew Howroyd_, Dec 06 2015

%Y Equals 2n*A000560 (and so 45 terms are known).

%K nonn

%O 1,2

%A _N. J. A. Sloane_

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)