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A254399 A Fibonacci sum: a(n) = Sum_{j=0..n-1} F(j)^2*F(2*n-j), in which the F's are the Fibonacci numbers. 1
0, 2, 8, 41, 179, 794, 3422, 14706, 62754, 267179, 1135079, 4817276, 20429252, 86600786, 367005092, 1555075557, 6588493275, 27912159494, 118245265874, 500914535330, 2121959178350, 8988897300407, 38077930682063, 161301621015576, 683287035188904 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Curtis Greene, Herbert S. Wilf, Closed form summation of C-finite sequences, arXiv:math/0405574 [math.CO], 2005.

Eric Weisstein's MathWorld, Fibonacci Number

Wikipedia, Fibonacci number

Index entries for linear recurrences with constant coefficients, signature (6,-4,-18,14,0,-1).

FORMULA

a(n) = (1/2)*(F(2*n) + F(n)^2*F(n+1) - F(n)*F(n+1)^2 + F(n+1)^3 - F(2*n+1)).

G.f.: -(x^5+x^4-4*x^3+2*x^2)/(-x^6+14*x^4-18*x^3-4*x^2+6*x-1). - Alois P. Heinz, Jan 30 2015

a(n) = 3*(-1)^n*F(n-1)/10 + (-1)^n*F(n)/10 - F(2*n-1)/2 + F(3*n+1)/5. - Ehren Metcalfe, Mar 25 2016

MATHEMATICA

F = Fibonacci; a[n_] := (1/2)*(F[2*n] + F[n]^2*F[n+1] - F[n]*F[n+1]^2 + F[n+1]^3 - F[2*n+1]); Array[a, 30]

PROG

(MAGMA) [(1/2)*(Fibonacci(2*n) + Fibonacci(n)^2*Fibonacci(n+1) - Fibonacci(n)*Fibonacci(n+1)^2 + Fibonacci(n+1)^3 - Fibonacci(2*n+1)): n in [1..25]]; // Vincenzo Librandi, Jan 30 2015

(PARI) concat(0, Vec(x^2*(1-x)*(2-2*x-x^2) / ((1-3*x+x^2)*(1+x-x^2)*(1-4*x-x^2)) + O(x^30))) \\ Colin Barker, Mar 26 2016

CROSSREFS

Cf. A000045.

Sequence in context: A012597 A012534 A092354 * A060436 A020083 A333093

Adjacent sequences:  A254396 A254397 A254398 * A254400 A254401 A254402

KEYWORD

easy,nonn

AUTHOR

Jean-Fran├žois Alcover, Jan 30 2015

STATUS

approved

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Last modified September 18 20:19 EDT 2020. Contains 337173 sequences. (Running on oeis4.)