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

1,2

Links

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

Formula

a(n) = Sum_{k=0..n-1} Fibonacci(k+2) * A023533(n-k), n >= 1. - 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 *)

Prog

(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
(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

Crossrefs

Essentially the same as A023613.

Cf. A000045, A023533.

Sequence in context: A262984 A201077 A355383 * A354210 A023561 A243735

Adjacent sequences: A023652 A023653 A023654 * A023656 A023657 A023658

Keyword

nonn

Author

Clark Kimberling

Status

approved