A025086 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A000045, t = A023533.

0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 988, 1598, 2586, 4184, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17712, 28658, 46370, 75028, 121398, 196426, 317824, 514250

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A000045, A023533.

Programs

Magma

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
A025086:= func< n | (&+[Fibonacci(k)*A023533(n+1-k): k in [1..Floor(n/2)]]) >;
[A025086(n): n in [2..100]]; // G. C. Greubel, Sep 08 2022

Mathematica

b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];
A025086[n_]:= A025086[n]= Sum[Fibonacci[n-j+1]*b[j], {j, Floor[(n+3)/2], n}];
Table[A025086[n], {n,2,100}] (* G. C. Greubel, Sep 08 2022 *)

SageMath

@CachedFunction
def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..10))
@CachedFunction
def A025086(n): return sum(fibonacci(n-j+1)*b(j) for j in (((n+3)//2)..n))
[A025086(n) for n in (2..100)] # G. C. Greubel, Sep 08 2022

Extensions

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