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Convolution of A023533 with itself.
10

%I #7 Jul 14 2022 12:08:48

%S 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,

%T 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,

%U 1,0,0,0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,2,0,0,2

%N Convolution of A023533 with itself.

%H G. C. Greubel, <a href="/A023670/b023670.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = Sum_{k=1..n} A023533(k)*A023533(n-k+1). - _G. C. Greubel_, Jul 14 2022

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

%t A023670[n_]:= Sum[A023533[k]*A023533[n+1-k], {k, n}];

%t Table[A023670[n], {n, 100}] (* _G. C. Greubel_, Jul 14 2022 *)

%o (Magma)

%o A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;

%o [(&+[A023533(k)*A023533(n-k+1): k in [1..n]]): n in [1..100]]; // _G. C. Greubel_, Jul 14 2022

%o (SageMath)

%o def A023533(n):

%o if binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n: return 0

%o else: return 1

%o [sum(A023533(k)*A023533(n-k+1) for k in (1..n)) for n in (1..100)] # _G. C. Greubel_, Jul 14 2022

%Y Cf. A023533.

%K nonn

%O 1,4

%A _Clark Kimberling_