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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; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..23.

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, 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, 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, Apr 18 2010]

Sequence in context: A181458 A069070 A174052 * A160282 A243803 A203855

Adjacent sequences:  A141525 A141526 A141527 * A141529 A141530 A141531

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula, Aug 11 2008

EXTENSIONS

An expansion of the toral inverse of the Euler prime generating polynomial

STATUS

approved

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Last modified March 25 21:19 EDT 2017. Contains 284111 sequences.