A024466 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (Fibonacci numbers), t = A023533.

1, 0, 0, 1, 1, 2, 3, 0, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 988, 1598, 2586, 4184, 6770, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17712, 28658, 46370, 75028, 121398, 196426

Offset

1,6

Links

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

Formula

a(n) = Sum_{k=1..floor((n+1)/2)} Fibonacci(k)*A023533(n+1-k).

Mathematica

A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3]!= n, 0, 1];
A024466[n_]:= A024466[n]= Sum[Fibonacci[j]*A023533[n-j+1], {j, Floor[(n+1)/2]}];
Table[A024466[n], {n, 100}] (* G. C. Greubel, Jul 25 2022 *)

Prog

(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[Fibonacci(k)*A023533(n+1-k): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // G. C. Greubel, Jul 25 2022
(SageMath)
@CachedFunction
def A023533(n): return 0 if (binomial(floor((6*n-1)^(1/3)) +2, 3)!= n) else 1
def A024466(n): return sum(fibonacci(j)*A023533(n-j+1) for j in (1..((n+1)//2)))
[A024466(n) for n in (1..100)] # G. C. Greubel, Jul 25 2022

Crossrefs

Cf. A000045, A023533.

Sequence in context: A083926 A218757 A261430 * A021817 A069585 A167613

Adjacent sequences: A024463 A024464 A024465 * A024467 A024468 A024469

Keyword

nonn

Author

Clark Kimberling

Status

approved