cp's OEIS Frontend

A025125 a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n-k+1), where k = floor(n/2), s = A023533.

%I A025125 #11 Jan 09 2023 07:40:57
%S A025125 0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,
%T A025125 0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,
%U A025125 0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
%N A025125 a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n-k+1), where k = floor(n/2), s = A023533.
%H A025125 G. C. Greubel, <a href="/A025125/b025125.txt">Table of n, a(n) for n = 1..5000</a>
%t A025125 b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];
%t A025125 A025125[n_]:= A025125[n]= Sum[b[n -j+1]*b[j+1], {j, Floor[(n+2)/2], n}];
%t A025125 Table[A025125[n], {n,130}] (* _G. C. Greubel_, Sep 14 2022 *)
%o A025125 (Magma)
%o A025125 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A025125 A025125:= func< n | (&+[A023533(k)*A023533(n+2-k): k in [1..Floor((n+1)/2)]]) >;
%o A025125 [A025125(n): n in [1..130]]; // _G. C. Greubel_, Sep 14 2022
%o A025125 (SageMath)
%o A025125 @CachedFunction
%o A025125 def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..15))
%o A025125 @CachedFunction
%o A025125 def A025125(n): return sum(b(n-j+1)*b(j+1) for j in (((n+2)//2)..n))
%o A025125 [A025125(n) for n in (1..130)] # _G. C. Greubel_, Sep 14 2022
%Y A025125 Cf. A023533.
%K A025125 nonn
%O A025125 1,138
%A A025125 _Clark Kimberling_