A001010 - OEIS

%I M0323 N0120 #59 Jul 13 2022 12:06:49

%S 1,2,2,4,6,8,18,20,56,48,178,132,574,348,1870,1008,6144,2812,20314,

%T 8420,67534,24396,225472,74756,755672,222556,2540406,693692,8564622,

%U 2107748,28941258,6656376,98011464,20548932

%N Number of symmetric foldings of a strip of n 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).

%H Jean-François Alcover, <a href="/A001010/b001010.txt">Table of n, a(n) for n = 1..52</a>

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

%H R. Dickau, <a href="/A001010/a001010.pdf">Symmetric Stamp Foldings</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 Frank Ruskey, <a href="http://combos.org/meander">Information on Stamp Foldings</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StampFolding.html">Stamp Folding.</a>

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

%F a(2n) = 2*A000682(n+2), a(2n+1) = 2*A007822(n). - _Sean A. Irvine_, Mar 18 2013

%t A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];

%t A007822 = Cases[Import["https://oeis.org/A007822/b007822.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := Which[n == 1, 1, EvenQ[n], 2*A000682[[n/2 + 1]], OddQ[n], 2*A007822[[(n - 1)/2 + 1]]];

%t Array[a, 52] (* _Jean-François Alcover_, Sep 03 2019, updated Jul 13 2022 *)

%Y Cf. A007822, A000682.

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_, _Stéphane Legendre_