A223093 Number of foldings of n labeled stamps in which leaf 1 is inwards and leaf n outwards (or leaf 1 outwards and leaf n inwards).

0, 0, 2, 4, 16, 38, 132, 342, 1144, 3134, 10370, 29526, 97458, 285458, 942920, 2822310, 9341008, 28440970, 94358558, 291294678, 968853072, 3025232480, 10086634316, 31797822936, 106265437078, 337731551446, 1131117792978, 3620119437762, 12148796744234, 39118879440938

Offset: 1

Author

N. J. A. Sloane, Mar 29 2013

Keywords

• nonn

Comments

Subset of foldings of n labeled stamps (A000136). - Stéphane Legendre, Apr 09 2013

Links

• Stéphane Legendre, Table of n, a(n) for n = 1..42
• 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.
• Index entries for sequences obtained by enumerating foldings

Programs

Mathematica

A000682 = Cases[Import["https://oeis.org/A000682/b000682.txt", "Table"], {, }][[All, 2]];
A077014 = Cases[Import["https://oeis.org/A077014/b077014.txt", "Table"], {, }][[All, 2]];
a[n_] := A000682[[n + 1]] - A077014[[n + 1]];
Array[a, 30] (* Jean-François Alcover, Sep 07 2019, after Andrew Howroyd *)

Formula

a(n) = A000682(n+1) - A077014(n). - Andrew Howroyd, Dec 06 2015

A217310(n) = 2*a(n) if n is odd and A217310(n) = a(n) if n is even. - Stéphane Legendre, Jan 09 2014

Extensions

Name clarified by Stéphane Legendre, Apr 09 2013

More terms from Stéphane Legendre, Apr 09 2013