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A278459 a(n) is the number of size n Eulerian orientations in L1(1). 1
1, 2, 10, 66, 466, 3458, 26650, 211458, 1716642, 14193282, 119115818, 1012129602, 8690293618, 75283480834, 657206992954, 5775816653314, 51060139789122, 453749755736834, 4051091496955978, 36319665678928962, 326850292861873426, 2951487063152265858, 26735348244277012570 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For definition of the set L1(k), k>=1, see sec. 3, def. 1 in N. Bonichon et al. paper; in sec. 3.2, (10) gives the quadratic equation for the g.f.

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..299

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 = 2*x*y^2 - (1-x)^2*y - x^2 - 2*x + 1.

EXAMPLE

A(x) = 1 + 2*x + 10*x^2 + 66*x^3 + 466*x^4 + 3458*x^5 + ... is the g.f.

MATHEMATICA

terms = 23;

A[_] = 0; Do[A[x_] = (1 - 2x - x^2 + 2x A[x]^2)/(1-x)^2 + O[x]^terms // Normal, {terms}];

CoefficientList[A[x], x][[1 ;; terms]] (* Jean-François Alcover, Jul 25 2018 *)

PROG

(PARI)

x='x; y='y; Fxy = 2*x*y^2 - (1-x)^2*y - x^2 - 2*x + 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: A064170 A151410 A230050 * A278461 A027307 A278460

Adjacent sequences:  A278456 A278457 A278458 * A278460 A278461 A278462

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Nov 22 2016

STATUS

approved

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Last modified September 18 09:59 EDT 2019. Contains 327170 sequences. (Running on oeis4.)