A242638 - OEIS

%I #13 Feb 24 2020 01:02:03

%S 0,0,2,10,47,226,1122,5738,30107,161460,882180,4897752,27570532,

%T 157083944,904523386,5257488138,30814928707,181966070440,

%U 1081790956890,6470568865530,38917734372615,235260687007290,1428777440333880,8714285083290072,53359037547384852

%N Number of quadrangulations of a hexagon b_1 w_3 b_2 w_1 b_3 w_2 having n inner faces and not containing the edge b_1 w_1.

%H Andrew Howroyd, <a href="/A242638/b242638.txt">Table of n, a(n) for n = 0..500</a>

%H Sergey Kitaev, Anna de Mier, Marc Noy, <a href="https://doi.org/10.1016/j.ejc.2013.06.013">On the number of self-dual rooted maps</a>, European J. Combin. 35, 2014, pp377-387, MR3090510.

%F G.f.: (2 - 6*g(x) + 3*g(x)^2)*g(x)^2/(1 - g(x))^4 where g(x)/x is the g.f. of A006013. - _Andrew Howroyd_, Feb 23 2020

%o (PARI) seq(n)={my(g=serreverse(x*(1-x)^2 + O(x^n))); Vec((2 - 6*g + 3*g^2)*g^2/(1 - g)^4, -(n+1))} \\ _Andrew Howroyd_, Feb 23 2020

%Y Cf. A006013, A242637.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, May 19 2014

%E Terms a(6) and beyond from _Andrew Howroyd_, Feb 23 2020