A361938 - OEIS

%I #36 Apr 08 2023 00:30:31

%S 1,0,1,1,4,10,42,156,792,3792,22920,133560,938880,6434640,51614640,

%T 406344960,3663676800,32560174080,326014657920,3227173488000,

%U 35531881459200,387590549472000,4654346740243200,55461310186867200,721387883125324800,9322190319746304000

%N a(0)=1, a(1)=0; a(n) = floor(n/2)*(a(n-1) + a(n-2)).

%C For n <= 1000000, n prime divides a(n) only when n=5 and n composite does not divide a(n) only when n = 9. Is this always so?

%F a(0)=1, a(1)=0; a(n) = floor(n/2)*(a(n-1) + a(n-2)).

%e a(0) = 1;

%e a(1) = 0;

%e a(2) = floor(2/2)*(a(1) + a(0)) = 1;

%e a(3) = floor(3/2)*(a(2) + a(1)) = 1;

%e a(4) = floor(4/2)*(a(3) + a(2)) = 4;

%e a(5) = floor(5/2)*(a(4) + a(3)) = 10.

%t a[0] = 1; a[1] = 0; a[n_] := a[n] = Floor[n/2] * (a[n - 1] + a[n - 2]); Array[a, 30, 0] (* _Amiram Eldar_, Apr 05 2023 *)

%o (Python)

%o def seqx_it(n):

%o   a0 = 1

%o   a1 = 0

%o   sequence_store = [a0,a1]

%o   for i in range (2,n):

%o     a2 = (i//2) * (a1 + a0)

%o     sequence_store.append(a2)

%o     a0 = a1

%o     a1 = a2

%o   return sequence_store

%Y Cf. A055596.

%K nonn

%O 0,5

%A _Davide Oliveri_, Mar 31 2023