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 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. 1
 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, 21, 23, 25, 27, 29, 32, 36, 40, 44, 48, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 FORMULA a(n) = Sum_{k=1..floor((n+1)/2)} A005408(k-1) * A023533(n-k+1). MATHEMATICA A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]]+2, 3]!= n, 0, 1]; A024601[n_]:= A024601[n]= Sum[(2*j-1)*A023533[n-j+1], {j, Floor[(n+1)/2]}]; Table[A024601[n], {n, 100}] (* G. C. Greubel, Aug 01 2022 *) PROG (Magma) A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >; [(&+[(2*k-1)*A023533(n+1-k): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // G. C. Greubel, Aug 01 2022 (SageMath) @CachedFunction def A023533(n): return 0 if (binomial(floor((6*n-1)^(1/3)) +2, 3)!= n) else 1 def A024601(n): return sum((2*j-1)*A023533(n-j+1) for j in (1..((n+1)//2))) [A024601(n) for n in (1..100)] # G. C. Greubel, Aug 01 2022 CROSSREFS Cf. A005408, A023533. Sequence in context: A099414 A004785 A099744 * A173013 A223174 A225401 Adjacent sequences: A024598 A024599 A024600 * A024602 A024603 A024604 KEYWORD nonn AUTHOR STATUS approved

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Last modified March 20 18:09 EDT 2023. Contains 361391 sequences. (Running on oeis4.)