A001010 -id:A001010 - cp's OEIS frontend

A178961 Partial sums of A001010.

1, 3, 5, 9, 15, 23, 41, 61, 117, 165, 343, 475, 1049, 1397, 3267, 4275, 10419, 13231, 33545, 41965, 109499, 133895, 359367, 434123, 1189795, 1412351, 3952757, 4646449, 13211071, 15318819, 44260077, 50916453, 148927917, 169476849

Offset: 1

Jonathan Vos Post, Dec 31 2010

Number of symmetric foldings of a strip of <= n stamps.

			a(13) = 1 + 2 + 2 + 4 + 6 + 8 + 18 + 20 + 56 + 48 + 178 + 132 + 574 = 1049 is prime.

Hunter Hogan, Table of n, a(n) for n = 1..52
Index entries for sequences obtained by enumerating foldings

Cf. A001010.

a(n) = Sum_{i=1..n} A001010(i).

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

Original entry on oeis.org

1, 1, 2, 5, 14, 38, 120, 353, 1148, 3527, 11622, 36627, 121622, 389560, 1301140, 4215748, 14146335, 46235800, 155741571, 512559195, 1732007938, 5732533570, 19423092113, 64590165281, 219349187968, 732358098471, 2492051377341, 8349072895553, 28459491475593

Offset: 1

N. J. A. Sloane, Stéphane Legendre

M. Gardner, Mathematical Games, Sci. Amer. Vol. 209 (No. 3, Mar. 1963), p. 262.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence - see entry 576, Fig. 17, and the front cover).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, Table of n, a(n) for n = 1..45 [from S. Legendre, 2013]
B. Bobier and J. Sawada, A fast algorithm to generate open meandric systems and meanders, Transactions on Algorithms, Vol. 6 No. 2 (2010) 12 pages.
S. P. Castell, Computer Puzzles, Computer Bulletin, March 1975, pages 3, 33, 34. [Annotated scanned copy]
CombOS - Combinatorial Object Server, Generate meanders and stamp foldings.
Santo Diano, Letter to N. J. A. Sloane, circa Dec 01 1979.
R. Dickau, Stamp Folding.
R. Dickau, Stamp Folding. [Cached copy, PDF format, with permission]
R. Dickau, Unlabeled Stamp Foldings.
R. Dickau, Unlabeled Stamp Foldings. [Cached copy, PDF format, with permission]
R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
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]
S. Legendre, Foldings and Meanders, arXiv preprint arXiv:1302.2025 [math.CO], 2013.
S. Legendre, Foldings and Meanders, Aust. J. Comb. 58(2), 275-291, 2014.
David Orden, In how many ways can you fold a strip of stamps?, 2014.
Frank Ruskey, Information on Stamp Foldings.
J. Sawada and R. Li, Stamp foldings, semi-meanders, and open meanders: fast generation algorithms, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).
N. J. A. Sloane, Illustration of initial terms. (Fig. 17 of the 1973 Handbook of Integer Sequences. The initial terms are also embossed on the front cover.)
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 2.
Eric Weisstein's World of Mathematics, Stamp Folding.
Index entries for sequences obtained by enumerating foldings

Cf. A000682, A086441.

A000136 = Import["https://oeis.org/A000136/b000136.txt", "Table"][[All, 2]];
A001010 = Cases[Import["https://oeis.org/A001010/b001010.txt", "Table"], {, }][[All, 2]];
a[n_] := If[n == 1, 1, (A001010[[n]] + A000136[[n]])/4];
Array[a, 45] (* Jean-François Alcover, Sep 04 2019 *)

a(n) = (A001010(n) + A000136(n)) / 4 for n >= 2. - Andrew Howroyd, Dec 07 2015

a(17) and a(20) corrected by Sean A. Irvine, Mar 17 2013

A007822 Number of symmetric foldings of 2n+1 stamps.

Original entry on oeis.org

1, 1, 3, 9, 28, 89, 287, 935, 3072, 10157, 33767, 112736, 377836, 1270203, 4282311, 14470629, 49005732, 166261653, 565055147, 1923186472, 6554868916, 22367933148, 76417819396, 261335128098, 894597454360, 3064970675173

Offset: 1

Stéphane Legendre

nonn

J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152.
Stéphane Legendre, Illustration of initial terms
S. Legendre, Foldings and Meanders, arXiv preprint arXiv:1302.2025, 2013.
S. Legendre, Foldings and Meanders, Aust. J. Comb. 58(2), 275-291, 2014.
W. F. Lunnon, A map-folding problem, Math. Comp. 22 (1968), 193-199.
Index entries for sequences obtained by enumerating foldings

Cf. A001010.

More terms from Stéphane Legendre (2013) added by N. J. A. Sloane, Mar 30 2013

cp's OEIS Frontend

A178961 Partial sums of A001010.

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

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A007822 Number of symmetric foldings of 2n+1 stamps.

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