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A207873 Numerator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial.

%I A207873 #6 Jul 12 2012 00:40:00
%S A207873 1,1,1,5,1,9,5,1,17,9,5,21,1,33,17,9,41,5,37,21,1,65,33,17,81,9,73,41,
%T A207873 5,69,37,21,85,1,129,65,33,161,17,145,81,9,137,73,41,169,5,133,69,37,
%U A207873 165,21,149,85,1,257,129,65,321,33,289,161,17,273,145,81,337
%N A207873 Numerator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial.
%C A207873 The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813.  See A207872 for denominators to match A207873.
%t A207873 fb[n_] := Block[{k = Ceiling[Log[GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k],
%t A207873     AppendTo[fr, 0]]; k--]; fr]; t = Table[fb[n],
%t A207873       {n, 1, 500}];
%t A207873 b[n_] := Reverse[Table[x^k, {k, 0, n}]]
%t A207873 p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
%t A207873 Table[p[n, x], {n, 1, 40}]
%t A207873 Denominator[Table[p[n, x] /. x -> 1/2,
%t A207873    {n, 1, 120}]]                       (* A207872 *)
%t A207873 Numerator[Table[p[n, x] /. x -> 1/2,
%t A207873    {n, 1, 120}]]                       (* A207873 *)
%Y A207873 Cf. A207813, A207873.
%K A207873 nonn
%O A207873 1,4
%A A207873 _Clark Kimberling_, Feb 21 2012