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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 (list; graph; refs; listen; history; text; internal format)
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+x-x^2)*(1-4*x-x^2)*(1-x)) (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

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Last modified December 5 16:13 EST 2021. Contains 349557 sequences. (Running on oeis4.)