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A147982
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A Fernandez-type expansion for a Slow chaotic sequence using A004001 and the modulo three A147952: f(n)=A147952(A004001(n)); p(x,n)=Product[x+f(n),{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)).
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0
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1, 1, 1, 2, 2, 4, 6, 8, 11, 16, 20, 28, 38, 50, 69, 92, 120, 154, 203, 261, 338, 437, 559, 710, 907, 1146, 1444, 1829, 2291, 2863, 3593, 4457, 5539, 6882, 8503, 10501, 12931, 15861, 19466, 23854, 29125, 35520, 43279, 52557, 63735, 77358, 93472, 112885
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| This sequence has ratio at n=100:1.1521476591741213.
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FORMULA
| f(n)=A147952(A004001(n)); ;p(x,n)=Product[x+f(n),{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)).
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MATHEMATICA
| (*A004001*) g[0] = 0; g[1] = 1; g[2] = 1; g[n_] := g[n] = g[g[n - 1]] + g[n - g[n - 1]]; (*A147952*) f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[f[n - 2]] + If[Mod[n, 3] == 0, f[f[n/3]], If[Mod[n, 3] ==1, f[f[(n - 1)/3]], f[n - f[(n - 2)/3]]]]; P[x_, n_] := P[x, n] = Product[1 + f[g[m]]*x^m, {m, 0, n}] Length[CoefficientList[ExpandAll[P[x, 99]], x]] a1 = CoefficientList[ExpandAll[P[x, 99]], x]; a2 = CoefficientList[ExpandAll[P[x, 100]], x]; a = Sum[If[a1[[n]] - a2[[n]] == 0, 1, 0], {n, 1, 4951}]; Table[a2[[n]], {n, 1, 100}]
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CROSSREFS
| Sequence in context: A145809 A116859 A179999 * A051466 A080015 A080054
Adjacent sequences: A147979 A147980 A147981 * A147983 A147984 A147985
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 18 2008
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