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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 Table of n, a(n) for n=1..21. 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 Cf. A179299, A228704. Sequence in context: A246963 A093460 A187613 * A199493 A245059 A321587 Adjacent sequences: A179297 A179298 A179299 * A179301 A179302 A179303 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.)