A223095 Number of foldings of n labeled stamps in which both end leaves are inwards.

0, 0, 0, 2, 10, 40, 156, 546, 1986, 6716, 23742, 79472, 277178, 925588, 3205896, 10711486, 36963722, 123712788, 426075994, 1429030624, 4916833424, 16526958144, 56840484232, 191466923584, 658460090994, 2222507917328, 7644360501390, 25850724646008, 88938175307354

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

Crossrefs

Cf. A000136, A000682, A077014.

Cf. A223093, A223094.

Programs

Mathematica

A217318 = Import["https://oeis.org/A217318/b217318.txt", "Table"][[All, 2]];
a[n_] := (2 - Mod[n, 2]) A217318[[n]];
Array[a, 42] (* Jean-François Alcover, Sep 02 2019 *)

Formula

a(n) = A223094(n) - A223093(n). - Andrew Howroyd, Dec 06 2015

a(n) = A000136(n) + A077014(n) - 2 * A000682(n). - Andrew Howroyd, Dec 06 2015

A217318(n) = a(n) if n is odd and A217318(n) = (1/2)*a(n) if n is even. - Stéphane Legendre, Jan 13 2014

Extensions

Name clarified by Stéphane Legendre, Apr 09 2013

More terms from Stéphane Legendre, Apr 09 2013