

A215038


Partial sums of A066259: a(n) = sum(F(k+1)^2*F(k),k=0..n), n>=0, with the Fibonacci numbers F=A000045.


1



0, 1, 5, 23, 98, 418, 1770, 7503, 31779, 134629, 570284, 2415788, 10233404, 43349461, 183631161, 777874251, 3295127934, 13958386366, 59128672790, 250473078515, 1061020985255, 4494557022121, 19039249069560, 80651553307128
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OFFSET

0,3


COMMENTS

For a derivation of the explicit form of this sum see the link under A215308 on the partial summation formula, eq. (7).


LINKS

Table of n, a(n) for n=0..23.


FORMULA

a(n) = sum(A066259(k),k=0..n) = sum(F(k+1)^2*F(k),k=0..n), n >= 0, with A066259(0)=0.
a(n) = (F(n+2)*F(n+1)^2  (1)^n*(F(n) + (1)^n)/2 = (A066258(n+1)  (1)^n*A008346(n))/2, n >= 0.
O.g.f.: x*(1+x)/((1+xx^2)*(14*xx^2)*(1x)) (from A066259).


EXAMPLE

a(2) = 0 + 1^2*1 + 2^2*1 = 1 + 4 = 5.


CROSSREFS

Cf. A001655, A215037.
Sequence in context: A109765 A323922 A119012 * A084615 A181331 A268400
Adjacent sequences: A215035 A215036 A215037 * A215039 A215040 A215041


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Aug 09 2012


STATUS

approved



