

A363754


a(n) = Sum_{k=0..n} F(2k1)*F(2k)*F(2k+1)/2, where F(n) is the Fibonacci number A000045(n).


1



0, 1, 16, 276, 4917, 88132, 1581196, 28372701, 509125596, 9135883240, 163936760185, 2941725767256, 52787126964456, 947226559367881, 16997290941068152, 305004010378316172, 5473074895864584141, 98210344115173624636, 1762313119177232976916, 31623425801074947486405
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OFFSET

0,3


COMMENTS

This is one of the triple Fibonacci sums that were considered by Subba Rao (1953).
Taking any of the given closedform expressions for a(n) with Fibonacci numbers, one can extend a(n) to negative indices by using the property F(n)=(1)^(n+1). This gives a(n)=a(n1).


LINKS



FORMULA

a(n) = (F(2n+1)^3 + F(2n+1)  2)/8.
a(n) = (F(6*n+3)+8*F(2*n+1)10)/40.
a(n) = 22*a(n1)  77*a(n2) + 77*a(n3)  22*a(n4) + a(n5).
G.f.: x*(1  6*x + x^2)/((1  x)*(1  3*x + x^2)*(1  18*x + x^2)).


MATHEMATICA

LinearRecurrence[{22, 77, 77, 22, 1}, {0, 1, 16, 276, 4917}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



