A223093 - OEIS

%I #44 Sep 08 2019 03:12:19

%S 0,0,2,4,16,38,132,342,1144,3134,10370,29526,97458,285458,942920,

%T 2822310,9341008,28440970,94358558,291294678,968853072,3025232480,

%U 10086634316,31797822936,106265437078,337731551446,1131117792978,3620119437762,12148796744234,39118879440938

%N 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).

%C Subset of foldings of n labeled stamps (A000136). - _Stéphane Legendre_, Apr 09 2013

%H Stéphane Legendre, <a href="/A223093/b223093.txt">Table of n, a(n) for n = 1..42</a>

%H S. Legendre, <a href="http://arxiv.org/abs/1302.2025">Foldings and Meanders</a>, arXiv preprint arXiv:1302.2025 [math.CO], 2013.

%H S. Legendre, <a href="http://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p275.pdf">Foldings and Meanders</a>, Aust. J. Comb. 58(2), 275-291, 2014.

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

%F a(n) = A000682(n+1) - A077014(n). - _Andrew Howroyd_, Dec 06 2015

%F A217310(n) = 2*a(n) if n is odd and A217310(n) = a(n) if n is even. - _Stéphane Legendre_, Jan 09 2014

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

%t A077014 = Cases[Import["https://oeis.org/A077014/b077014.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := A000682[[n + 1]] - A077014[[n + 1]];

%t Array[a, 30] (* _Jean-François Alcover_, Sep 07 2019, after _Andrew Howroyd_ *)

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Mar 29 2013

%E Name clarified by _Stéphane Legendre_, Apr 09 2013

%E More terms from _Stéphane Legendre_, Apr 09 2013