A023670 Convolution of A023533 with itself.

1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A023533.

Programs

Magma

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[A023533(k)*A023533(n-k+1): k in [1..n]]): n in [1..100]]; // G. C. Greubel, Jul 14 2022

Mathematica

A023533[n_]:= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3] != n, 0, 1];
A023670[n_]:= Sum[A023533[k]*A023533[n+1-k], {k, n}];
Table[A023670[n], {n, 100}] (* G. C. Greubel, Jul 14 2022 *)

SageMath

def A023533(n):
    if binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n: return 0
    else: return 1
[sum(A023533(k)*A023533(n-k+1) for k in (1..n)) for n in (1..100)] # G. C. Greubel, Jul 14 2022

Formula

a(n) = Sum_{k=1..n} A023533(k)*A023533(n-k+1). - G. C. Greubel, Jul 14 2022