A278461 a(n) is the number of size n Eulerian orientations in L2(1).

1, 2, 10, 66, 490, 3898, 32482, 279882, 2473362, 22294194, 204174842, 1894462354, 17771064186, 168254374890, 1605751354066, 15431016952730, 149191682979874, 1450182228623458, 14163576408858346, 138924886089370082, 1367918804901854218, 13516246001650813338, 133977227356098512834

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

Cf. A277493.

Sequence in context: A230050 A340467 A278459 * A372580 A027307 A373325

Adjacent sequences: A278458 A278459 A278460 * A278462 A278463 A278464

Keyword

nonn

Author

Gheorghe Coserea, Nov 23 2016

Status

approved