|
| |
|
|
A141528
|
|
A Fibonacci Binet type sequence made from the roots of the Euler prime generating polynomial:(A005846) x^2+x+41 ; a=(-1-Sqrt[163]*i)/2; b=(-1+Sqrt[163]*i)/2; a(n)=(a^n-b^n)/(I*Sqrt[163).
|
|
0
| |
|
|
0, -1, 1, 40, -81, -1559, 4880, 59039, -259119, -2161480, 12785359, 75835321, -600035040, -2509213121, 27110649761, 75767088200, -1187303728401, -1919146887799, 50598599752240, 28086422647519, -2102629012489359, 951085683941080, 85256703828122639
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
FORMULA
| a=(-1-Sqrt[163]*i)/2; b=(-1+Sqrt[163]*i)/2; a(n)=(a^n-b^n)/(I*Sqrt[163).
a(n)=expansion(1/(41*x^2+x+1)) [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 18 2010]
|
|
|
MATHEMATICA
| a = x /. Solve[x^2 + x + 41 == 0, x][[1]]; b = x /. Solve[x^2 + x + 41 == 0, x][[2]]; f[n_] = (a^n - b^n)/(I*Sqrt[163]); Table[ExpandAll[f[n]], {n, 0, 50}]
Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 18 2010: (Start)
p[x_] = x^2 + x + 41;
q[x_] = ExpandAll[x^2*p[1/x]];
Table[SeriesCoefficient[Series[1/q[x], {x, 0, 50}], m], {m, 0, 50}] (End)
|
|
|
CROSSREFS
| Cf. A005846.
Cf. A005846 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 18 2010]
Sequence in context: A181458 A069070 A174052 * A160282 A203855 A188335
Adjacent sequences: A141525 A141526 A141527 * A141529 A141530 A141531
|
|
|
KEYWORD
| uned,sign
|
|
|
AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 11 2008
|
|
|
EXTENSIONS
| An expansion of the toral inverse of the Euler prime generating polynomial
|
| |
|
|
