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A179300 a(n) is the number of corner-rooted hexangulations of girth 6 with n inner faces. 2
1, 3, 17, 128, 1131, 11070, 116317, 1287480, 14829188, 176250143, 2148687567, 26750057584, 338939419026, 4359422270652, 56799490825125, 748414965684808, 9959308633462092, 133694287642377756, 1808762770097970724, 24642635223262953600, 337856475305856870275 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
O. Bernardi and É. Fusy, A bijection for triangulations, quadrangulations, pentagulations, etc., J. Combin. Theory Ser. A 119 (2012), 218-244.
O. Bernardi and É. Fusy, A bijection for triangulations, quadrangulations, pentagulations, etc., arXiv:1007.1292 [math.CO], 2010-2011.
J. Bouttier and E. Guitter, A note on irreducible maps with several boundaries, arXiv:1305.4816 [math.CO], 2013.
William G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964), 746-768.
William G. Brown, Enumeration of quadrangular dissections of the disk, Canad. J. Math., 17 (1965) 302-317
W. T. Tutte, A Census of Planar Maps, Canad. J. Math. 15 (1963), 249-271.
FORMULA
Bouttier-Guittier give an explicit formula.
a(1) = 1, and a(n) = (6*(2*(-2 + n))!/((-2 + n)!*n!))*2F1(-5*n, 2 - n, 2*(2 - n); -1) for n >= 2, where 2F1(a, b, c; z) is the hypergeometric function. - Franck Maminirina Ramaharo, Jan 27 2019
a(n) ~ sqrt(152 - 62*sqrt(6)) * (248*sqrt(6)/9 - 52)^n / (3*sqrt(Pi) * n^(5/2)). - Vaclav Kotesovec, Jun 09 2019
EXAMPLE
G.f.: x + 3*x^2 + 17*x^3 + 128*x^4 + 1131*x^5 + 11070*x^6 + ...
MATHEMATICA
Join[{1}, Table[(6*(2*(-2 + n))!/((-2 + n)!*n!))*Hypergeometric2F1[-5*n, 2 - n, 2*(2 - n), -1], {n, 2, 50}]] (* Franck Maminirina Ramaharo, Jan 27 2019 *)
CROSSREFS
Sequence in context: A246963 A093460 A187613 * A199493 A245059 A321587
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Jul 09 2010
EXTENSIONS
Edited by N. J. A. Sloane, Sep 06 2013
More terms from Franck Maminirina Ramaharo, Jan 27 2019
STATUS
approved

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Last modified April 17 08:05 EDT 2024. Contains 371756 sequences. (Running on oeis4.)