A156133 Denominator coefficients of infinite over the Fibonacci sequence: p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Denominator(p(x,n)).

1, -1, 1, 1, 1, -2, -2, 1, 1, -3, -6, 3, 1, 1, -4, -19, -4, 1, -1, 8, 40, -60, -40, 8, 1, 1, -13, -104, 260, 260, -104, -13, 1, 1, -21, -273, 1092, 1820, -1092, -273, 21, 1, 1, -33, -747, 3894, 16270, 3894, -747, -33, 1, -1, 55, 1870, -19635, -85085, 136136, 85085

Offset

0,6

Comments

Row sums are:

{1, 1, -2, -4, -25, -44, 288, 1276, 22500, 96976, -1707552,...}.

The denominator and numerator polynomials appear to be new.

Links

Table of n, a(n) for n=0..57.

Formula

p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Denominator(p(x,n)).

Example

{1},
{-1, 1, 1},
{1, -2, -2, 1},
{1, -3, -6, 3, 1},
{1, -4, -19, -4, 1},
{-1, 8, 40, -60, -40, 8, 1},
{1, -13, -104, 260, 260, -104, -13, 1},
{1, -21, -273, 1092, 1820, -1092, -273, 21, 1},
{1, -33, -747, 3894, 16270, 3894, -747, -33, 1},
{-1, 55, 1870, -19635, -85085, 136136, 85085, -19635, -1870, 55, 1},
{1, -89, -4895, 83215, 582505, -1514513, -1514513, 582505, 83215, -4895, -89, 1}

Mathematica

Clear[t0, p, x, n, m];
p[x_, n_] = (1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]
Table[Denominator[FullSimplify[ExpandAll[p[x, n]]]], {n, 0, 10}];
Flatten[%]

Crossrefs

A000045, A055870

Sequence in context: A308497 A010358 A155865 * A010048 A055870 A360208

Adjacent sequences: A156130 A156131 A156132 * A156134 A156135 A156136

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Feb 04 2009

Status

approved