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A278461
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a(n) is the number of size n Eulerian orientations in L2(1).
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1
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1, 2, 10, 66, 490, 3898, 32482, 279882, 2473362, 22294194, 204174842, 1894462354, 17771064186, 168254374890, 1605751354066, 15431016952730, 149191682979874, 1450182228623458, 14163576408858346, 138924886089370082, 1367918804901854218, 13516246001650813338, 133977227356098512834
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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 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.
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LINKS
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FORMULA
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G.f. y satisfies: 0 = x^2*y^3 + x*(x-4)*y^2 + (2*x+1)*y - 1.
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EXAMPLE
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1 + 2*x + 10*x^2 + 66*x^3 + 490*x^4 + 3898*x^5 + ...
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MATHEMATICA
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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}];
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PROG
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(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)
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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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