cp's OEIS Frontend

A001010 Number of symmetric foldings of a strip of n stamps.

%I A001010 M0323 N0120 #69 Aug 24 2025 04:24:11
%S A001010 1,2,2,4,6,8,18,20,56,48,178,132,574,348,1870,1008,6144,2812,20314,
%T A001010 8420,67534,24396,225472,74756,755672,222556,2540406,693692,8564622,
%U A001010 2107748,28941258,6656376,98011464,20548932,332523306,65573260,1130110294,205022836,3846372944,659806116,13109737832,2084555444,44735866296,6755838520
%N A001010 Number of symmetric foldings of a strip of n stamps.
%D A001010 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001010 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001010 Jean-François Alcover, <a href="/A001010/b001010.txt">Table of n, a(n) for n = 1..52</a>
%H A001010 R. Dickau, <a href="http://www.robertdickau.com/symmetricfoldings.html">Symmetric Stamp Foldings</a>
%H A001010 R. Dickau, <a href="/A001010/a001010.pdf">Symmetric Stamp Foldings</a> [Cached copy, pdf format, with permission]
%H A001010 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 A001010 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 A001010 Frank Ruskey, <a href="http://combos.org/meander">Information on Stamp Foldings</a>
%H A001010 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StampFolding.html">Stamp Folding.</a>
%H A001010 <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>
%F A001010 a(1) = 1, a(2n-1) = 2*A007822(n), a(2n) = 2*A000682(n+1). - _Sean A. Irvine_, Mar 18 2013; corrected by _Hunter Hogan_, Aug 08 2025
%t A001010 A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];
%t A001010 A007822 = Cases[Import["https://oeis.org/A007822/b007822.txt", "Table"], {_, _}][[All, 2]];
%t A001010 a[n_] := Which[n == 1, 1, EvenQ[n], 2*A000682[[n/2 + 1]], OddQ[n], 2*A007822[[(n - 1)/2 + 1]]];
%t A001010 Array[a, 52] (* _Jean-François Alcover_, Sep 03 2019, updated Jul 13 2022 *)
%Y A001010 Cf. A007822, A000682.
%K A001010 nonn,nice,changed
%O A001010 1,2
%A A001010 _N. J. A. Sloane_, _Stéphane Legendre_