OFFSET
0,4
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..1000
Nicolas Bonichon, Éric Fusy, Benjamin Lévêque, A bijection for essentially 3-connected toroidal maps, arXiv:1907.04016 [math.CO], 2019.
FORMULA
G.f.: A^2*(1+A)/((1+2*A)*(1-A)^2*(1+3*A)) where A=x*(1+A)^2.
G.f.: x*(1 + 8*x + (2*x - 1)*sqrt(1 - 4*x))/(2*(2 + x)*(1 - 4*x)*(3 + 4*x)). - Vaclav Kotesovec, Jun 25 2019
a(n) ~ 2^(2*n - 3) / 3. - Vaclav Kotesovec, Jun 25 2019
MAPLE
dev_A := 0; n := 20; dev_A := series(RootOf(A-x*(1+A)^2, A), x = 0, n+1);
seq(coeff(series(subs(A = dev_A, A^2*(1+A)/((1+2*A)*(1-A)^2*(1+3*A))), x, n+1), x, k), k = 0 .. n);
# second Maple program:
a:= proc(n) option remember; `if`(n<6, [0, 0, 1, 2, 11, 40][n+1],
((37*n^2-258*n+401)*a(n-1)-6*(2*n^2-25*n+88)*a(n-2)
-48*(3*n^2-23*n+45)*a(n-3)-32*(n-4)*(2*n-7)*a(n-4))
/((6*(n-1))*(n-5)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Jun 07 2019
MATHEMATICA
CoefficientList[Series[x*(1 + 8*x + (2*x - 1)*Sqrt[1 - 4*x])/(2*(2 + x)*(1 - 4*x)*(3 + 4*x)), {x, 0, 30}], x] (* Vaclav Kotesovec, Jun 25 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Nicolas Bonichon, Jun 05 2019
STATUS
approved