A025126 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A023533, t = A014306.

1, 1, 0, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A014306, A023533.

Cf. A024693. [From R. J. Mathar, Oct 23 2008]

Programs

Magma

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
A025126:= func< n | (&+[(1-A023533(n+2-k))*A023533(k): k in [1..Floor((n+1)/2)]]) >;
[A025126(n): n in [1..130]]; // G. C. Greubel, Sep 14 2022

Mathematica

b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];
A025126[n_]:= A025126[n]= Sum[(1-b[j+1])*b[n-j+1], {j, Floor[(n+2)/2], n}];
Table[A025126[n], {n,130}] (* G. C. Greubel, Sep 14 2022 *)

SageMath

@CachedFunction
def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..15))
@CachedFunction
def A025126(n): return sum((1-b(j+1))*b(n-j+1) for j in (((n+2)//2)..n))
[A025126(n) for n in (1..130)] # G. C. Greubel, Sep 14 2022