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, 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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A005408, A023533.

Programs

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

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 *)

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

Formula

a(n) = Sum_{k=1..floor((n+1)/2)} A005408(k-1) * A023533(n-k+1).