cp's OEIS Frontend

A024601 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (odd natural numbers), t = A023533.

%I A024601 #6 Aug 01 2022 18:37:47
%S A024601 1,0,0,1,3,5,7,0,0,1,3,5,7,9,11,13,15,17,19,1,3,5,7,9,11,13,15,17,19,
%T A024601 21,23,25,27,29,32,36,40,44,48,11,13,15,17,19,21,23,25,27,29,31,33,35,
%U A024601 37,39,41,44,48,52,56,60,64,68,72,76,80,84,88,92,96,29,31,33,35,37,39,41,43,45,47
%N A024601 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (odd natural numbers), t = A023533.
%H A024601 G. C. Greubel, <a href="/A024601/b024601.txt">Table of n, a(n) for n = 1..5000</a>
%F A024601 a(n) = Sum_{k=1..floor((n+1)/2)} A005408(k-1) * A023533(n-k+1).
%t A024601 A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1,3]]+2, 3]!= n, 0,1];
%t A024601 A024601[n_]:= A024601[n]= Sum[(2*j-1)*A023533[n-j+1], {j, Floor[(n+1)/2]}];
%t A024601 Table[A024601[n], {n, 100}] (* _G. C. Greubel_, Aug 01 2022 *)
%o A024601 (Magma)
%o A024601 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A024601 [(&+[(2*k-1)*A023533(n+1-k): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // _G. C. Greubel_, Aug 01 2022
%o A024601 (SageMath)
%o A024601 @CachedFunction
%o A024601 def A023533(n): return 0 if (binomial(floor((6*n-1)^(1/3)) +2, 3)!= n) else 1
%o A024601 def A024601(n): return sum((2*j-1)*A023533(n-j+1) for j in (1..((n+1)//2)))
%o A024601 [A024601(n) for n in (1..100)] # _G. C. Greubel_, Aug 01 2022
%Y A024601 Cf. A005408, A023533.
%K A024601 nonn
%O A024601 1,5
%A A024601 _Clark Kimberling_