OFFSET
1,1
COMMENTS
The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813.
MATHEMATICA
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],
AppendTo[fr, 0]]; k--]; fr]; t = Table[fb[n],
{n, 1, 500}];
b[n_] := Reverse[Table[x^k, {k, 0, n}]]
p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
Table[p[n, x], {n, 1, 40}]
t2 = Table[p[n, x] /. x -> I, {n, 1, 420}];
Flatten[Position[t2, 0] (* A207871 *)
Denominator[Table[p[n, x] /. x -> 1/2,
{n, 1, 120}]] (* A207872 *)
Numerator[Table[p[n, x] /. x -> 1/2,
{n, 1, 120}]] (* A207873 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 21 2012
STATUS
approved