%I #7 Jul 26 2022 01:36:28

%S 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,

%T 144,233,377,610,988,1598,2586,4184,6770,8,13,21,34,55,89,144,233,377,

%U 610,987,1597,2584,4181,6765,10946,17712,28658,46370,75028,121398,196426

%N 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.

%H G. C. Greubel, <a href="/A024466/b024466.txt">Table of n, a(n) for n = 1..5000</a>

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

%t A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1,3]] +2,3]!= n,0,1];

%t A024466[n_]:= A024466[n]= Sum[Fibonacci[j]*A023533[n-j+1], {j, Floor[(n+1)/2]}];

%t Table[A024466[n], {n, 100}] (* _G. C. Greubel_, Jul 25 2022 *)

%o (Magma)

%o A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;

%o [(&+[Fibonacci(k)*A023533(n+1-k): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // _G. C. Greubel_, Jul 25 2022

%o (SageMath)

%o @CachedFunction

%o def A023533(n): return 0 if (binomial(floor((6*n-1)^(1/3)) +2, 3)!= n) else 1

%o def A024466(n): return sum(fibonacci(j)*A023533(n-j+1) for j in (1..((n+1)//2)))

%o [A024466(n) for n in (1..100)] # _G. C. Greubel_, Jul 25 2022

%Y Cf. A000045, A023533.

%K nonn

%O 1,6

%A _Clark Kimberling_