A179299 Number of corner-rooted pentagulations of girth 5 with 2n+1 inner faces.

1, 5, 121, 4690, 228065, 12673173, 768897585, 49645423227, 3357669088200, 235393836387360, 16981887962145418, 1254065444086727685, 94424981678123285373, 7227272422780512414100, 560989900421822288646265, 44076648941211191411236261, 3500015582480750626266664105

Offset: 0

Author

Jonathan Vos Post, Jul 09 2010

Keywords

• nonn

Links

• Olivier Bernardi and Éric Fusy, A bijection for triangulations, quadrangulations, pentagulations, etc, Journal of Combinatorial Theory, Series A 119, 1 (2012) 218-244; arXiv:1007.1292 [math.CO], 2010-2011.
• 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.

Crossrefs

Cf. A069271, A001764, A179300.

Programs

Mathematica

k = 34;
{w0, w1, w2, w3} = FixedPoint[Function[{w0, w1, w2, w3}, {w1^2 + w2, w1^3 + 2 w1 w2 + w3, w1^4 + 3 w1^2 w2 + 2 w1 w3 + w2^2, x (1 + w0)^4} + O[x]^k] @@ # &, ConstantArray[0, 4]];
f = w3 - (w0 w3 + 2 w1 w2);
CoefficientList[f, x][[2 ;; ;; 2]]
(* Andrey Zabolotskiy, Jan 17 2022 *)

Extensions

Entry edited, terms a(5) and beyond added by Andrey Zabolotskiy, Jan 17 2022