|
Search: id:A156133
|
|
|
| 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)). |
|
+0
2
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
Row sums are:
{1, 1, -2, -4, -25, -44, 288, 1276, 22500, 96976, -1707552,...}.
The denominator and numerator polynomials appear to be new.
|
|
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
Sequence in context: A131791 A010358 A155865 this_sequence A010048 A055870 A088459
Adjacent sequences: A156130 A156131 A156132 this_sequence A156134 A156135 A156136
|
|
KEYWORD
|
sign,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 04 2009
|
|
|
Search completed in 0.002 seconds
|
