A025109 - OEIS

A025109

a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = (F(2), F(3), F(4), ...), t = A023533.

0, 0, 1, 2, 3, 0, 0, 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1598, 2586, 4184, 6770, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28658, 46370, 75028, 121398, 196426, 317824, 514250

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 2..5000

FORMULA

a(n) = Sum_{k=1..floor(n/2)} Fibonacci(k+1)*A023533(n-k+1).

MATHEMATICA

A023533[n_]:= If[Binomial[Floor[Surd[6*n-1, 3]] + 2, 3] != n, 0, 1];

A025109[n_]:= A025109[n]= Sum[Fibonacci[k+1]*A023533[n+1-k], {k, Floor[n/2]}];

Table[A025109[n], {n, 2, 100}] (* G. C. Greubel, Jul 14 2022 *)

PROG