OFFSET
0,4
REFERENCES
A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003
FORMULA
a(n) = Sum_{k=2..n} C(k,2)*F(k), where F(n) = A000045(n), the Fibonacci numbers and C(n, 2) = A000217(n-1), the triangular numbers, n(n-1)/2.
a(n) = C(n,2) F(n+2) - n F(n+3) + F(n+5) - 5.
G.f.: x^2(1 + 3x + x^3)/((1 - x)(1 - x - x^2)^3).
a(n)-a(n-1) = A086926(n). - R. J. Mathar, May 16 2025
MATHEMATICA
Binomial[n, 2]Fibonacci[n + 2] - n Fibonacci[n + 3] + Fibonacci[n + 5] - 5
PROG
(PARI) a(n) = sum(k=2, n, k*(k-1)*fibonacci(k)/2); \\ Michel Marcus, Feb 28 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mitch Harris, Feb 28 2006
STATUS
approved
