cp's OEIS Frontend

A024375 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023532, t = A023533.

%I A024375 #7 Sep 07 2022 18:18:43
%S A024375 1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,
%T A024375 2,1,2,2,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,2,1,2,2,1,1,2,2,1,2,2,2,2,
%U A024375 0,1,1,1,1,1,0,1,1,1,1,1,1,0,1,2,1,2,2,1,2,1
%N A024375 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023532, t = A023533.
%H A024375 G. C. Greubel, <a href="/A024375/b024375.txt">Table of n, a(n) for n = 1..5000</a>
%t A024375 A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3] != n, 0, 1];
%t A024375 A023532[n_]:= If[IntegerQ[(Sqrt[8*n+9] -3)/2], 0, 1];
%t A024375 A025375[n_]:= A025075[n]= Sum[A023532[j]*A023533[n-j+1], {j, Floor[(n+1)/2]}];
%t A024375 Table[A025375[n], {n, 130}] (* _G. C. Greubel_, Sep 07 2022 *)
%o A024375 (Magma)
%o A024375 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A024375 A023532:= func< n |  IsSquare(8*n+9) select 0 else 1 >;
%o A024375 A025375:= func< n | (&+[A023532(k)*A023533(n+1-k): k in [1..Floor((n+1)/2)]]) >;
%o A024375 [A025375(n): n in [1..130]]; // _G. C. Greubel_, Sep 07 2022
%o A024375 (SageMath)
%o A024375 @CachedFunction
%o A024375 def A023533(n): return 0 if (binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n) else 1
%o A024375 def A023532(n): return 0 if is_square(8*n+9) else 1
%o A024375 def A025375(n): return sum(A023532(k)*A023533(n-k+1) for k in (1..((n+1)//2)))
%o A024375 [A025375(n) for n in (1..130)] # _G. C. Greubel_, Sep 07 2022
%Y A024375 Cf. A023532, A023533.
%K A024375 nonn
%O A024375 1,35
%A A024375 _Clark Kimberling_