OFFSET
0,3
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..499
Nicolas Bonichon, Éric Fusy, Benjamin Lévêque, A bijection for essentially 3-connected toroidal maps, arXiv:1907.04016 [math.CO], 2019.
Éric Fusy, Benjamin Lévêque, Orientations and bijections for toroidal maps with prescribed face-degrees and essential girth, arXiv:1807.00522 [math.CO], 2018. See Proposition 25 p. 37.
FORMULA
G.f.: A/(1-3*A)^2 where A=x(1+A)^4 is the g.f. of A002293.
From Vaclav Kotesovec, Jun 25 2019: (Start)
Recurrence: 81*(n-1)*(3*n - 2)*(3*n - 1)*(24*n - 37)*a(n) = 24*(13824*n^4 - 59328*n^3 + 92832*n^2 - 62278*n + 14653)*a(n-1) - 2048*(2*n - 3)*(4*n - 7)*(4*n - 5)*(24*n - 13)*a(n-2).
a(n) ~ 2^(8*n - 3) / 3^(3*n). (End)
MAPLE
n:=20:
dev_A := series(RootOf(A-x*(1+A)^4, A), x = 0, n+1):
seq(coeff(series(subs(A=dev_A, A/(1-3*A)^2), x, n+1), x, k), k=0..n);
MATHEMATICA
terms = 21;
A[_] = 0; Do[A[x_] = x (1 + A[x])^4 + O[x]^terms, terms];
CoefficientList[A[x]/(1 - 3 A[x])^2, x] (* Jean-François Alcover, Jun 17 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Nicolas Bonichon, Jun 05 2019
STATUS
approved