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A207822 Number of distinct irreducible factors of n-th Zeckendorf polynomial. 0
0, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 2, 2, 3, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 2, 2, 1, 2, 3, 2, 1, 2, 3, 3, 2, 2, 1, 2, 3, 1, 2, 2, 1, 2, 2, 2, 2, 3, 3, 1, 3, 1, 1, 3, 3, 1, 3, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 1, 2, 3, 2, 2, 1, 3, 2, 2, 2, 1, 4, 3, 1, 2, 3, 2, 1, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813.
LINKS
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
Cf. A207813.
Sequence in context: A288915 A175062 A139767 * A343068 A057555 A075532
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved

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Last modified March 4 23:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)