A024865 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A000027, t = A023533.

0, 0, 1, 2, 3, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 21, 23, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..5000

Crossrefs

Cf. A000027, A023533.

Programs

Magma

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
A024865:= func< n | (&+[k*A023533(n+1-k): k in [1..Floor(n/2)]]) >;
[A024865(n): n in [2..130]]; // G. C. Greubel, Sep 07 2022

Mathematica

A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3] != n, 0, 1];
A024865[n_]:= A024865[n]= Sum[j*A023533[n-j+1], {j, Floor[n/2]}];
Table[A024865[n], {n, 2, 130}] (* G. C. Greubel, Sep 07 2022 *)

SageMath

@CachedFunction
def A023533(n): return 0 if (binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n) else 1
def A024865(n): return sum(k*A023533(n-k+1) for k in (1..(n//2)))
[A024865(n) for n in (2..130)] # G. C. Greubel, Sep 07 2022