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.

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, 23, 25, 27, 29, 32, 36, 40, 44, 9, 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, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53

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 >;
A025115:= func< n | (&+[(2*k-1)*A023533(n+2-k): k in [1..Floor((n+1)/2)]]) >;
[A025115(n): n in [1..100]]; // G. C. Greubel, Sep 13 2022

Mathematica

b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];
A025115[n_]:= A025115[n]= Sum[(2*(n-j+2)-1)*b[j], {j, Floor[(n+4)/2], n+1}];
Table[A025115[n], {n,100}] (* G. C. Greubel, Sep 13 2022 *)

SageMath

@CachedFunction
def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..10))
@CachedFunction
def A025115(n): return sum((2*(n-j+2)-1)*b(j) for j in (((n+4)//2)..n+1))
[A025115(n) for n in (1..100)] # G. C. Greubel, Sep 13 2022