A228704 Number of 4-irreducible maps made up of two hexagons and n squares.

1, 6, 21, 62, 180, 540, 1683, 5418, 17901, 60390, 207207, 720954, 2537964, 9023328, 32354910, 116873028, 424901655, 1553574330, 5709123135, 21075032250, 78114397680, 290595385080, 1084663520730, 4060907367660, 15246207481050, 57387012171372, 216517061206998

Offset: 0

Author

N. J. A. Sloane, Sep 06 2013

Keywords

• nonn
• easy

Links

• J. Bouttier and E. Guitter, A note on irreducible maps with several boundaries, arXiv preprint, arXiv:1305.4816 [math.CO], 2013.

Crossrefs

Cf. A179300.

Programs

Mathematica

Join[{1}, Table[6*(2*(n - 1))!/(n!*(n - 1)!)*Hypergeometric2F1[-5, 1 - n, 2*(1 - n), -1], {n, 1, 50}]] (* Franck Maminirina Ramaharo, Jan 27 2019 *)

Formula

Bouttier-Guittier give an explicit formula.

a(0) = 1, and a(n) = (6*(2 *(n - 1))!/(n!*(n - 1)!))*2F1(-5, 1 - n, 2*(1 - n); -1) for n >= 1, where 2F1(a, b, c; z) is the hypergeometric function. - Franck Maminirina Ramaharo, Jan 27 2019

a(n) ~ 729 * 2^(2*n - 6) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Jun 09 2019

D-finite with recurrence n*(9*n-29)*(3*n-10)*a(n) -2*(9*n-20)*(2*n-7)*(3*n-7)*a(n-1)=0. - R. J. Mathar, Feb 08 2021

Extensions

More terms from Franck Maminirina Ramaharo, Jan 27 2019