A023655 Convolution of (F(2), F(3), F(4), ...) and A023533.

1, 2, 3, 6, 10, 16, 26, 42, 68, 111, 180, 291, 471, 762, 1233, 1995, 3228, 5223, 8451, 13675, 22127, 35802, 57929, 93731, 151660, 245391, 397051, 642442, 1039493, 1681935, 2721428, 4403363, 7124791

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..4700

Crossrefs

Essentially the same as A023613.

Cf. A000045, A023533.

Programs

Magma

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[Fibonacci(k+2)*A023533(n-k): k in [0..n-1]]): n in [1..50]]; // G. C. Greubel, Jul 16 2022

Mathematica

Table[Sum[Fibonacci[m+1 -Binomial[j+3,3]], {j,0,n}], {n,0,5}, {m, Binomial[n+3,3] +1, Binomial[n+4,3]}]//Flatten (* G. C. Greubel, Jul 16 2022 *)

SageMath

def A023655(n, k): return sum(fibonacci(k+1-binomial(j+3,3)) for j in (0..n))
flatten([[A023655(n, k) for k in (binomial(n+3,3)+1..binomial(n+4,3))] for n in (0..5)]) # G. C. Greubel, Jul 16 2022

Formula

a(n) = Sum_{k=0..n-1} Fibonacci(k+2) * A023533(n-k), n >= 1. - G. C. Greubel, Jul 16 2022