cp's OEIS Frontend

A025115 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A005408 (odd natural numbers), t = A023533.

%I A025115 #9 Sep 15 2022 06:24:35
%S A025115 0,0,1,3,5,0,0,0,1,3,5,7,9,11,13,15,17,0,1,3,5,7,9,11,13,15,17,19,21,
%T A025115 23,25,27,29,32,36,40,44,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,
%U A025115 39,41,44,48,52,56,60,64,68,72,76,80,84,88,92,27,29,31,33,35,37,39,41,43,45,47,49,51,53
%N A025115 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A005408 (odd natural numbers), t = A023533.
%H A025115 G. C. Greubel, <a href="/A025115/b025115.txt">Table of n, a(n) for n = 1..5000</a>
%t A025115 b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];
%t A025115 A025115[n_]:= A025115[n]= Sum[(2*(n-j+2)-1)*b[j], {j, Floor[(n+4)/2], n+1}];
%t A025115 Table[A025115[n], {n,100}] (* _G. C. Greubel_, Sep 13 2022 *)
%o A025115 (Magma)
%o A025115 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A025115 A025115:= func< n | (&+[(2*k-1)*A023533(n+2-k): k in [1..Floor((n+1)/2)]]) >;
%o A025115 [A025115(n): n in [1..100]]; // _G. C. Greubel_, Sep 13 2022
%o A025115 (SageMath)
%o A025115 @CachedFunction
%o A025115 def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..10))
%o A025115 @CachedFunction
%o A025115 def A025115(n): return sum((2*(n-j+2)-1)*b(j) for j in (((n+4)//2)..n+1))
%o A025115 [A025115(n) for n in (1..100)] # _G. C. Greubel_, Sep 13 2022
%Y A025115 Cf. A005408, A023533.
%K A025115 nonn
%O A025115 1,4
%A A025115 _Clark Kimberling_