cp's OEIS Frontend

A024595 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (F(2), F(3), ...), t = A023533.

%I A024595 #7 Jul 14 2022 05:51:11
%S A024595 1,0,0,1,2,3,5,0,0,1,2,3,5,8,13,21,34,55,89,1,2,3,5,8,13,21,34,55,89,
%T A024595 144,233,377,610,987,1598,2586,4184,6770,10954,13,21,34,55,89,144,233,
%U A024595 377,610,987,1597,2584,4181,6765,10946,17711,28658,46370,75028,121398,196426
%N A024595 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (F(2), F(3), ...), t = A023533.
%H A024595 G. C. Greubel, <a href="/A024595/b024595.txt">Table of n, a(n) for n = 1..5000</a>
%F A024595 a(n) = Sum_{k=1..floor((n+1)/2)} Fibonacci(k+1)*A023533(n-k+1).
%t A024595 A023533[n_]:= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3] != n, 0, 1];
%t A024595 A024595[n_]:= A024595[n]= Sum[Fibonacci[k+1]*A023533[n+1-k], {k, Floor[(n+1)/2]}];
%t A024595 Table[A024595[n], {n,100}] (* _G. C. Greubel_, Jul 14 2022 *)
%o A024595 (Magma)
%o A024595 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A024595 [(&+[Fibonacci(k+1)*A023533(n-k+1): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // _G. C. Greubel_, Jul 14 2022
%o A024595 (SageMath)
%o A024595 def A023533(n):
%o A024595     if binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n: return 0
%o A024595     else: return 1
%o A024595 [sum(fibonacci(k+1)*A023533(n-k+1) for k in (1..((n+1)//2))) for n in (1..100)] # _G. C. Greubel_, Jul 14 2022
%Y A024595 Cf. A000045, A023533, A023613.
%K A024595 nonn
%O A024595 1,5
%A A024595 _Clark Kimberling_