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A084205
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G.f. A(x) defined by: A(x)^5 consists entirely of integer coefficients between 1 and 5 (A083945); A(x) is the unique power series solution with A(0)=1.
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3
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1, 1, -1, 3, -8, 24, -76, 252, -854, 2950, -10343, 36706, -131570, 475576, -1731357, 6342042, -23356185, 86421603, -321111661, 1197586539, -4481348585, 16819759474, -63302097780, 238835017492, -903165412289, 3422512973645, -12994514592311, 49425252955926
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OFFSET
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0,4
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COMMENTS
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Limit a(n)/a(n+1) -> r = -0.2512525316047635 where A(r)=0.
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LINKS
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MATHEMATICA
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kmax = 30;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^5 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 5, 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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