|
|
A156135
|
|
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(Numerator(p(x,n)).
|
|
0
|
|
|
1, 0, -1, 1, 0, 1, -2, 1, 0, 1, -3, 1, 1, 0, 1, -4, -4, 1, 0, -1, 8, 9, -23, 6, 1, 0, 1, -13, -41, 106, -41, -13, 1, 0, 1, -21, -146, 484, -152, -186, 19, 1, 0, 1, -33, -492, 1784, 1784, -492, -33, 1, 0, -1, 55, 1359, -10701, -8552, 27128, -7875, -1467, 53, 1, 0, 1, -89
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,7
|
|
COMMENTS
|
Row sums are:
{1, 0, 0, 0, -6, 0, 0, 0, 2520, 0, 0,...}.
The denominator and numerator polynomials appear to be new.
|
|
LINKS
|
|
|
FORMULA
|
p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Numerator(p(x,n)).
|
|
EXAMPLE
|
{1},
{0, -1, 1},
{0, 1, -2, 1},
{0, 1, -3, 1, 1},
{0, 1, -4, -4, 1},
{0, -1, 8, 9, -23, 6, 1},
{0, 1, -13, -41, 106, -41, -13, 1},
{0, 1, -21, -146, 484, -152, -186, 19, 1},
{0, 1, -33, -492, 1784, 1784, -492, -33, 1},
{0, -1, 55, 1359, -10701, -8552, 27128, -7875, -1467, 53, 1},
{0, 1, -89, -3872, 50193, 117271, -327008, 117271, 50193, -3872, -89, 1}
|
|
MATHEMATICA
|
Clear[t0, p, x, n, m];
p[x_, n_] = (1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]
Table[Numerator[FullSimplify[ExpandAll[p[x, n]]]], {n, 0, 10}];
Table[CoefficientList[Numerator[FullSimplify[ExpandAll[p[x, n]]]], x], {n, 0, 10}];
Flatten[%]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|