A025096 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A000032, t = A023533.

0, 0, 1, 3, 4, 0, 0, 0, 1, 3, 4, 7, 11, 18, 29, 47, 76, 0, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2208, 3574, 5782, 9356, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39604, 64082, 103686, 167768, 271454

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A000032, A023533.

Programs

Magma

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
A025096:= func< n | (&+[Lucas(k)*A023533(n+1-k): k in [1..Floor(n/2)]]) >;
[A025096(n): n in [2..130]]; // G. C. Greubel, Sep 08 2022

Mathematica

A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1,3]] +2,3]!= n,0,1];
A025096[n_]:= A025096[n]= Sum[LucasL[j]*A023533[n-j+1], {j, Floor[n/2]}];
Table[A025096[n], {n,2,100}] (* G. C. Greubel, Sep 08 2022 *)

SageMath

@CachedFunction
def A023533(n): return 0 if (binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n) else 1
def A025096(n): return sum(lucas_number2(k,1,-1)*A023533(n-k+1) for k in (1..(n//2)))
[A025096(n) for n in (2..100)] # G. C. Greubel, Sep 08 2022

Extensions

Offset corrected by G. C. Greubel, Sep 08 2022