A023613 - OEIS

%I #24 Sep 22 2025 16:00:27

%S 1,1,2,4,6,10,16,26,42,69,111,180,291,471,762,1233,1995,3228,5223,

%T 8452,13675,22127,35802,57929,93731,151660,245391,397051,642442,

%U 1039493,1681935,2721428,4403363,7124791

%N Convolution of Fibonacci numbers and A023533.

%H Danny Rorabaugh, <a href="/A023613/b023613.txt">Table of n, a(n) for n = 0..4000</a>

%F a(n) = Sum_{k=1..n+1} A000045(k)*A023533(n+2-k). - _Danny Rorabaugh_, Mar 13 2015

%t Join[{1,1}, Table[Sum[Fibonacci[m+2 -Binomial[j+3,3]], {j,0,n}], {n,6}, {m, Binomial[n+3,3] -2, Binomial[n+4,3] -3}]]//Flatten (* _G. C. Greubel_, Jul 14 2022 *)

%o (SageMath) #Assuming A023533 is available as an array

%o for n in range(34):

%o     print(n, sum([A023533[k]*fibonacci(n+2-k) for k in range(1,n+2)]))

%o # _Danny Rorabaugh_, Mar 14 2015

%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+2-k): k in [1..n+1]]): n in [0..50]]; // _G. C. Greubel_, Jul 14 2022

%Y Cf. A000045, A023533.

%K nonn

%O 0,3

%A _Clark Kimberling_