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A278461 a(n) is the number of size n Eulerian orientations in L2(1). 1
1, 2, 10, 66, 490, 3898, 32482, 279882, 2473362, 22294194, 204174842, 1894462354, 17771064186, 168254374890, 1605751354066, 15431016952730, 149191682979874, 1450182228623458, 14163576408858346, 138924886089370082, 1367918804901854218, 13516246001650813338, 133977227356098512834 (list; graph; refs; listen; history; text; internal format)
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: A151410 A230050 A278459 * A027307 A278460 A278462

Adjacent sequences:  A278458 A278459 A278460 * A278462 A278463 A278464

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Nov 23 2016

STATUS

approved

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Last modified October 13 22:25 EDT 2019. Contains 327983 sequences. (Running on oeis4.)