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A084204
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G.f. A(x) defined by: A(x)^4 consists entirely of integer coefficients between 1 and 4 (A083954); 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, -7, 20, -58, 177, -554, 1769, -5739, 18866, -62684, 210146, -709882, 2413743, -8253995, 28366316, -97916761, 339326189, -1180068800, 4116957243, -14404398636, 50530280752, -177684095927, 626181400993, -2211215950469, 7823025701314, -27724997048327
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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 = -0.269562488839799 where A(r)=0.
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LINKS
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MAPLE
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g:= 1: a[0]:= 1:
for n from 1 to 50 do
a[n]:= -floor((coeff(g^4, x, n)-1)/4);
g:= g + a[n]*x^n;
od:
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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]^4 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1}; coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 4, 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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