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A025126 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A023533, t = A014306.

%I A025126 #9 Sep 15 2022 06:24:20
%S A025126 1,1,0,1,1,1,2,2,1,2,2,1,2,2,2,2,2,2,2,3,3,2,3,3,3,3,3,2,3,3,3,3,3,2,
%T A025126 3,3,2,3,4,4,4,4,3,4,4,4,4,4,4,4,4,4,3,4,3,4,4,3,4,4,4,4,4,3,4,4,4,4,
%U A025126 5,5,5,5,5,4,5,5,5,5,5,5,5,5,4,5,5,4,5,5,4,5,5,4,5,5,5,5,5,5,5,5,5,4,5,5,5,5,5,5,5,5,6
%N A025126 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A023533, t = A014306.
%H A025126 G. C. Greubel, <a href="/A025126/b025126.txt">Table of n, a(n) for n = 1..5000</a>
%t A025126 b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];
%t A025126 A025126[n_]:= A025126[n]= Sum[(1-b[j+1])*b[n-j+1], {j, Floor[(n+2)/2], n}];
%t A025126 Table[A025126[n], {n,130}] (* _G. C. Greubel_, Sep 14 2022 *)
%o A025126 (Magma)
%o A025126 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A025126 A025126:= func< n | (&+[(1-A023533(n+2-k))*A023533(k): k in [1..Floor((n+1)/2)]]) >;
%o A025126 [A025126(n): n in [1..130]]; // _G. C. Greubel_, Sep 14 2022
%o A025126 (SageMath)
%o A025126 @CachedFunction
%o A025126 def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..15))
%o A025126 @CachedFunction
%o A025126 def A025126(n): return sum((1-b(j+1))*b(n-j+1) for j in (((n+2)//2)..n))
%o A025126 [A025126(n) for n in (1..130)] # _G. C. Greubel_, Sep 14 2022
%Y A025126 Cf. A014306, A023533.
%Y A025126 Cf. A024693. [From _R. J. Mathar_, Oct 23 2008]
%K A025126 nonn
%O A025126 1,7
%A A025126 _Clark Kimberling_