A217474 Sequence used for the formula for partial sums of odd powers of even-indexed Fibonacci numbers.

-1, 2, -14, 278, -15016, 2172632, -835765304, 851104689248, -2288258540319136, 16212819419809777952, -302332135138133434911104, 14824259801049378686209605248, -1909922987705772492088576593195136, 646210649409632730922299328304587407872

Offset

0,2

Comments

This is the sequence c(m) used in the formula of Ozeki and Prodinger (see the references in A217472) for sum(F(2*k)^(2*m+1),k=1..n), m>=0, m>=0, given in A217472.

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = pL(n)*C(n), with pL(n)=A217473(n) and C(n) = (1/5^n)*sum((-1)^(j-1)*binomial(2*n+1,j)*F(2*(n-j)+1)/L(2*(n-j)+1),j=0..n), n>=0, with F=A000045 and L=A000032.

Example

a(2) = (1*4*11)*(-(1/25)*F(5)/L(5) + (1/5)*F(3)/(3) - (2/5)*F(1)/L(1)) = (1*4*11)*(-7/22) = -14.

Crossrefs

Sequence in context: A156910 A279117 A018803 * A132695 A015015 A355132

Adjacent sequences: A217471 A217472 A217473 * A217475 A217476 A217477

Keyword

sign,easy

Author

Wolfdieter Lang, Oct 12 2012

Status

approved