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

1,4

Links

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

Formula

a(n) = Sum_{k=1..n} A023533(k)*A023533(n-k+1). - 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 *)

Prog

(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
(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

Crossrefs

Cf. A023533.

Sequence in context: A103612 A083913 A363855 * A284394 A188170 A363805

Adjacent sequences: A023667 A023668 A023669 * A023671 A023672 A023673

Keyword

nonn

Author

Clark Kimberling

Status

approved