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A207872 Denominator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial. 5
1, 2, 4, 4, 8, 8, 8, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Zeckendorf polynomials Z(x,n) are defined and ordered at A207813.  Each power 2^k appears F(k+1) times, where F=A000045 (Fibonacci numbers).

LINKS

Table of n, a(n) for n=1..59.

Sajed Haque, Discriminators of Integer Sequences, Thesis, 2017, See p. 36.

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}]

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

Cf. A207813, A207873.

Sequence in context: A062383 A034583 A076347 * A140513 A265322 A188112

Adjacent sequences:  A207869 A207870 A207871 * A207873 A207874 A207875

KEYWORD

nonn,frac

AUTHOR

Clark Kimberling, Feb 21 2012

STATUS

approved

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)