OFFSET
1,6
COMMENTS
The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813.
EXAMPLE
Z(10,n) = x^4 + x = x(x + 1)(x^2 - x + 1), so a(10)=3.
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]]]]
TableForm[Table[{n, p[n, x], FactorList[p[n, x]]},
{n, 1, 10}]]
Table[-1 + Length[FactorList[p[n, x]]], {n, 1, 120}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved