A224317 - OEIS

%I #25 Aug 05 2023 23:27:21

%S 1,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,

%T 3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,0,2,3,

%U 0,2,3,0,2,3,0,2,3,0,2,3,0,2

%N a(n) = a(n-1) + 3 - a(n-1)!.

%C a(0) is taken as 1. The sequence remains essentially the same for a(0)=0,1,2,3.

%C Even though each term is dependent on the previous term, the sequence is repetitive.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).

%F a(n) = a(n-1) + 3 - a(n-1)!.

%F For n > 1, a(n) = (5+4*cos(2*(n+1)*Pi/3) - 2*sqrt(3)*sin(2*(n+1)*Pi/3))/3. - _Wesley Ivan Hurt_, Sep 27 2017

%F a(n) = (floor((4*n - 1)/3) + signum(n - 1)) mod 4. - _Lechoslaw Ratajczak_, Jul 01 2023

%e For n=1, a(1) = a(1-1) + 3 - a(1-1)! = 1 + 3 - 1 = 3.

%e For n=2, a(2) = a(2-1) + 3 - a(2-1)! = 3 + 3 - 6 = 0.

%e For n=3, a(3) = a(3-1) + 3 - a(3-1)! = 0 + 3 - 1 = 2.

%t NestList[#+3-#!&,1,90] (* or *) PadRight[{1},90,{2,3,0}] (* _Harvey P. Dale_, Apr 23 2015 *)

%o (PARI) a(n)=if(n>1, [0, 2, 3][n%3+1], 1) \\ _Charles R Greathouse IV_, Apr 03 2013

%K nonn,easy

%O 1,2

%A _Mihir Mathur_, Apr 03 2013