cp's OEIS Frontend

A001011 Number of ways to fold a strip of n blank stamps.

%I A001011 M1455 N0576 #140 Aug 25 2025 10:52:53
%S A001011 1,1,2,5,14,38,120,353,1148,3527,11622,36627,121622,389560,1301140,
%T A001011 4215748,14146335,46235800,155741571,512559195,1732007938,5732533570,
%U A001011 19423092113,64590165281,219349187968,732358098471,2492051377341,8349072895553,28459491475593
%N A001011 Number of ways to fold a strip of n blank stamps.
%D A001011 M. Gardner, Mathematical Games, Sci. Amer. Vol. 209 (No. 3, Mar. 1963), p. 262.
%D A001011 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence - see entry 576, Fig. 17, and the front cover).
%D A001011 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001011 N. J. A. Sloane, <a href="/A001011/b001011.txt">Table of n, a(n) for n = 1..45</a> [from S. Legendre, 2013]
%H A001011 B. Bobier and J. Sawada, <a href="http://www.cis.uoguelph.ca/~sawada/papers/meander.pdf">A fast algorithm to generate open meandric systems and meanders</a>, Transactions on Algorithms, Vol. 6 No. 2 (2010) 12 pages.
%H A001011 S. P. Castell, <a href="/A001011/a001011_3.pdf">Computer Puzzles</a>, Computer Bulletin, March 1975, pages 3, 33, 34. [Annotated scanned copy]
%H A001011 CombOS - Combinatorial Object Server, <a href="http://combos.org/meander">Generate meanders and stamp foldings</a>.
%H A001011 Santo Diano, <a href="/A001011/a001011_2.pdf">Letter to N. J. A. Sloane, circa Dec 01 1979</a>.
%H A001011 R. Dickau, <a href="http://www.robertdickau.com/stampfolding.html">Stamp Folding</a>.
%H A001011 R. Dickau, <a href="/A000136/a000136_2.pdf">Stamp Folding</a>. [Cached copy, PDF format, with permission]
%H A001011 R. Dickau, <a href="http://www.robertdickau.com/unlabeledfoldings.html">Unlabeled Stamp Foldings</a>.
%H A001011 R. Dickau, <a href="/A001011/a001011_1.pdf">Unlabeled Stamp Foldings</a>. [Cached copy, PDF format, with permission]
%H A001011 R. K. Guy, <a href="/A005347/a005347.pdf">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
%H A001011 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 A001011 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 A001011 S. Legendre, <a href="http://arxiv.org/abs/1302.2025">Foldings and Meanders</a>, arXiv preprint arXiv:1302.2025 [math.CO], 2013.
%H A001011 S. Legendre, <a href="http://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p275.pdf">Foldings and Meanders</a>, Aust. J. Comb. 58(2), 275-291, 2014.
%H A001011 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 A001011 Frank Ruskey, <a href="http://combos.org/meander">Information on Stamp Foldings</a>.
%H A001011 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 A001011 N. J. A. Sloane, <a href="/A001011/a001011.pdf">Illustration of initial terms</a>. (Fig. 17 of the 1973 Handbook of Integer Sequences. The initial terms are also embossed on the front cover.)
%H A001011 N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).
%H A001011 N. J. A. Sloane, <a href="https://arxiv.org/abs/2301.03149">"A Handbook of Integer Sequences" Fifty Years Later</a>, arXiv:2301.03149 [math.NT], 2023, p. 2.
%H A001011 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StampFolding.html">Stamp Folding</a>.
%H A001011 <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>
%F A001011 a(n) = (A001010(n) + A000136(n)) / 4 for n >= 2. - _Andrew Howroyd_, Dec 07 2015
%t A001011 A000136 = Import["https://oeis.org/A000136/b000136.txt", "Table"][[All, 2]];
%t A001011 A001010 = Cases[Import["https://oeis.org/A001010/b001010.txt", "Table"], {_, _}][[All, 2]];
%t A001011 a[n_] := If[n == 1, 1, (A001010[[n]] + A000136[[n]])/4];
%t A001011 Array[a, 45] (* _Jean-François Alcover_, Sep 04 2019 *)
%Y A001011 Cf. A000682, A086441.
%K A001011 nonn,nice,changed
%O A001011 1,3
%A A001011 _N. J. A. Sloane_, _Stéphane Legendre_
%E A001011 a(17) and a(20) corrected by _Sean A. Irvine_, Mar 17 2013