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A278462 a(n) is the number of size n Eulerian orientations in L2(2). 1
1, 2, 10, 66, 504, 4148, 35794, 319384, 2922472, 27273568, 258591700, 2483951402, 24121423518, 236417231844, 2335648036770, 23234567806722, 232536604918010, 2339766365713070, 23655013692855212, 240175288588925992, 2447961627258995826, 25037715732340569328, 256899046844874628732 (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, (21) gives the degree-6 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 = 2*x^5*y^6 - x^4*(x+8)*y^5 - x^3*(3*x^2-16)*y^4 + x^2*(2*x+3)*(2*x-5)*y^3 - x*(2*x^2-7*x-7)*y^2 - (5*x+1)*y + 1.

EXAMPLE

A(x) = 1 + 2*x + 10*x^2 + 66*x^3 + 504*x^4 + 4148*x^5 + ... is the g.f.

MATHEMATICA

terms = 23;

A[_] = 0; Do[A[x_] = (1/(1 + 5x))(1 + (7x + 7x^2 - 2x^3) A[x]^2 + (-15x^2 - 4x^3 + 4x^4) A[x]^3 + (16x^3 - 3x^5) A[x]^4 + (-8x^4 - x^5) A[x]^5 + 2x^5 A[x]^6) + 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^5*y^6 - x^4*(x+8)*y^5 - x^3*(3*x^2-16)*y^4 + x^2*(2*x+3)*(2*x-5)*y^3 - x*(2*x^2-7*x-7)*y^2 - (5*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: A278461 A027307 A278460 * A060206 A277493 A108205

Adjacent sequences:  A278459 A278460 A278461 * A278463 A278464 A278465

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Nov 23 2016

STATUS

approved

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Last modified September 20 03:51 EDT 2019. Contains 327210 sequences. (Running on oeis4.)