OFFSET
0,2
COMMENTS
For definition of the set L2(k), k>=1, see sec. 4, def. 6 in N. Bonichon et al. paper; in sec. 4.2, (19) gives the cubic equation for the g.f.
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 0..300
Nicolas Bonichon, Mireille Bousquet-Mélou, Paul Dorbec, Claire Pennarun, On the number of planar Eulerian orientations, arXiv:1610.09837 [math.CO], 2016.
FORMULA
G.f. y satisfies: 0 = x^2*y^3 + x*(x-4)*y^2 + (2*x+1)*y - 1.
EXAMPLE
1 + 2*x + 10*x^2 + 66*x^3 + 490*x^4 + 3898*x^5 + ...
MATHEMATICA
terms = 23;
A[_] = 0; Do[A[x_] = (-1 - 4x A[x]^2 + x^2 A[x]^2 + x^2 A[x]^3)/(-1 - 2x) + O[x]^terms // Normal, {terms}];
CoefficientList[A[x], x][[1 ;; terms]] (* Jean-François Alcover, Jul 25 2018 *)
PROG
(PARI)
x='x; y='y; Fxy = x^2*y^3 + x*(x-4)*y^2 + (2*x+1)*y - 1;
seq(N) = {
my(y0 = 1 + O('x^N), y1=0);
for (k = 1, N,
y1 = y0 - subst(Fxy, y, y0)/subst(deriv(Fxy, y), y, y0);
if (y1 == y0, break()); y0 = y1);
Vec(y0);
};
seq(23)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Nov 23 2016
STATUS
approved