A024595 - OEIS

A024595

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

1, 0, 0, 1, 2, 3, 5, 0, 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1598, 2586, 4184, 6770, 10954, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28658, 46370, 75028, 121398, 196426

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OFFSET

1,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

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

MATHEMATICA

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

A024595[n_]:= A024595[n]= Sum[Fibonacci[k+1]*A023533[n+1-k], {k, Floor[(n+1)/2]}];

Table[A024595[n], {n, 100}] (* G. C. Greubel, Jul 14 2022 *)

PROG