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A084207
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G.f. A(x) defined by: A(x)^7 consists entirely of integer coefficients between 1 and 7 (A083947); A(x) is the unique power series solution with A(0)=1.
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3
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1, 1, -2, 8, -34, 158, -768, 3858, -19851, 104023, -552974, 2973832, -16146688, 88376636, -487034106, 2699839758, -15043262970, 84197804254, -473140314356, 2668221663736, -15095165871964, 85645090974518, -487190919969502
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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 = -0.166670835025545 where A(r)=0.
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LINKS
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Table of n, a(n) for n=0..22.
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MATHEMATICA
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kmax = 25;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^7 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 7, a[k-1], Integers] // ToRules];
coes = coes /. r, {k, 3, kmax + 1}];
Table[a[k], {k, 0, kmax}] /. r (* Jean-François Alcover, Jul 26 2018 *)
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CROSSREFS
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Cf. A083947, A084202-A084206, A084208-A084212.
Sequence in context: A150898 A150899 A150900 * A151305 A150901 A046649
Adjacent sequences: A084204 A084205 A084206 * A084208 A084209 A084210
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna, May 20 2003
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STATUS
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approved
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