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A084209
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G.f. A(x) defined by: A(x)^9 consists entirely of integer coefficients between 1 and 9 (A083949); A(x) is the unique power series solution with A(0)=1.
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2
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1, 1, -3, 15, -85, 523, -3367, 22371, -152104, 1052568, -7385756, 52410754, -375382683, 2709626768, -19688989762, 143885743077, -1056748051734, 7795106129504, -57723430872280, 428923406694402
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OFFSET
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0,3
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COMMENTS
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Limit a(n)/a(n+1) --> r = -0.126715878986521 where A(r)=0.
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LINKS
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MATHEMATICA
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kmax = 20;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^9 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 9, a[k-1], Integers] // ToRules];
coes = coes /. r, {k, 3, kmax + 1}];
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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