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A278459
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a(n) is the number of size n Eulerian orientations in L1(1).
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1
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1, 2, 10, 66, 466, 3458, 26650, 211458, 1716642, 14193282, 119115818, 1012129602, 8690293618, 75283480834, 657206992954, 5775816653314, 51060139789122, 453749755736834, 4051091496955978, 36319665678928962, 326850292861873426, 2951487063152265858, 26735348244277012570
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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G.f. y satisfies: 0 = 2*x*y^2 - (1-x)^2*y - x^2 - 2*x + 1.
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EXAMPLE
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A(x) = 1 + 2*x + 10*x^2 + 66*x^3 + 466*x^4 + 3458*x^5 + ... is the g.f.
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MATHEMATICA
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terms = 23;
A[_] = 0; Do[A[x_] = (1 - 2x - x^2 + 2x A[x]^2)/(1-x)^2 + O[x]^terms // Normal, {terms}];
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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