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Search: id:A147879
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| A147879 |
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A Fernandez-type expansion for Hofstadter's A005185: p(x,n)=Product[x+A005185[n],{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)). |
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1
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| 1, 1, 1, 3, 5, 8, 12, 21, 29, 49, 73, 105, 162, 236, 338, 502, 706, 984, 1441, 1998, 2800, 3934, 5472, 7407, 10210, 14053, 19066, 25986, 35134, 47010, 63739, 85008, 112610, 150861, 200133, 264838, 349587, 459970, 602763, 792220, 1034136, 1345530
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The resulting polynomial is equivalent to and 1/q(x) type expansion of q(x)=x^n*f(1/x) and that expansion has a limiting ratio ( largest positive root) near:1.2154435489599418 or smaller: Table[N[a2[[n + 1]]/a2[[n]]], {n, 1, 99}]. The result is just slightly smaller than the A0004001 Conway ratio.
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EXAMPLE
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p(x,n)=Product[x+A005185[n],{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)).
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MATHEMATICA
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(*A005185*) f[n_Integer?Positive] := f[n] = f[n - f[n - 1]] + f[n - f[n - 2]]; f[0] = 0; f[1] = f[2] = 1; P[x_, n_] := P[x, n] = Product[1 + f[m] *x^m, {m, 0, n}]; a2 = CoefficientList[ExpandAll[P[x, 100]], x]; Table[a2[[n]], {n, 1, 100}]
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CROSSREFS
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A147559, A147654, A147655, A004001, A147869, A147871, A147665, A005185
Sequence in context: A020745 A004398 A055606 this_sequence A147880 A020643 A092360
Adjacent sequences: A147876 A147877 A147878 this_sequence A147880 A147881 A147882
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 16 2008
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