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

1, 2, 2, 4, 6, 8, 18, 20, 56, 48, 178, 132, 574, 348, 1870, 1008, 6144, 2812, 20314, 8420, 67534, 24396, 225472, 74756, 755672, 222556, 2540406, 693692, 8564622, 2107748, 28941258, 6656376, 98011464, 20548932, 332523306, 65573260, 1130110294, 205022836, 3846372944, 659806116, 13109737832, 2084555444, 44735866296, 6755838520

Offset: 1

Author

N. J. A. Sloane, Stéphane Legendre

Keywords

• nonn
• nice
• changed

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..52
• R. Dickau, Symmetric Stamp Foldings
• R. Dickau, Symmetric Stamp Foldings [Cached copy, pdf format, with permission]
• J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152.
• J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152. [Annotated, corrected, scanned copy]
• Frank Ruskey, Information on Stamp Foldings
• Eric Weisstein's World of Mathematics, Stamp Folding.
• Index entries for sequences obtained by enumerating foldings

Crossrefs

Cf. A007822, A000682.

Programs

Mathematica

A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];
A007822 = Cases[Import["https://oeis.org/A007822/b007822.txt", "Table"], {, }][[All, 2]];
a[n_] := Which[n == 1, 1, EvenQ[n], 2*A000682[[n/2 + 1]], OddQ[n], 2*A007822[[(n - 1)/2 + 1]]];
Array[a, 52] (* Jean-François Alcover, Sep 03 2019, updated Jul 13 2022 *)

Formula

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