cp's OEIS Frontend

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.

%I A024466 #7 Jul 26 2022 01:36:28
%S A024466 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 A024466 144,233,377,610,988,1598,2586,4184,6770,8,13,21,34,55,89,144,233,377,
%U A024466 610,987,1597,2584,4181,6765,10946,17712,28658,46370,75028,121398,196426
%N 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.
%H A024466 G. C. Greubel, <a href="/A024466/b024466.txt">Table of n, a(n) for n = 1..5000</a>
%F A024466 a(n) = Sum_{k=1..floor((n+1)/2)} Fibonacci(k)*A023533(n+1-k).
%t A024466 A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1,3]] +2,3]!= n,0,1];
%t A024466 A024466[n_]:= A024466[n]= Sum[Fibonacci[j]*A023533[n-j+1], {j, Floor[(n+1)/2]}];
%t A024466 Table[A024466[n], {n, 100}] (* _G. C. Greubel_, Jul 25 2022 *)
%o A024466 (Magma)
%o A024466 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A024466 [(&+[Fibonacci(k)*A023533(n+1-k): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // _G. C. Greubel_, Jul 25 2022
%o A024466 (SageMath)
%o A024466 @CachedFunction
%o A024466 def A023533(n): return 0 if (binomial(floor((6*n-1)^(1/3)) +2, 3)!= n) else 1
%o A024466 def A024466(n): return sum(fibonacci(j)*A023533(n-j+1) for j in (1..((n+1)//2)))
%o A024466 [A024466(n) for n in (1..100)] # _G. C. Greubel_, Jul 25 2022
%Y A024466 Cf. A000045, A023533.
%K A024466 nonn
%O A024466 1,6
%A A024466 _Clark Kimberling_