A021337 - OEIS

%I #27 Dec 27 2023 08:36:15

%S 0,0,3,0,0,3,0,0,3,0,0,3,0,0,3,0,0,3,0,0,3,0,0,3,0,0,3,0,0,3,0,0,3,0,

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

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

%N Decimal expansion of 1/333.

%H Vincenzo Librandi, <a href="/A021337/b021337.txt">Table of n, a(n) for n = 0..1000</a>

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

%F G.f.: 3*x^2/(1 - x^3). - _Chai Wah Wu_, Jun 21 2016

%F From _Wesley Ivan Hurt_, Jul 02 2016: (Start)

%F a(n) = a(n-3) for n>2.

%F a(n) = 1 - cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3).

%F a(n) = 3*(1 - sgn((n+1) mod 3)).

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

%p seq(op([0, 0, 3]), n=0..50); # _Wesley Ivan Hurt_, Jul 02 2016

%t PadLeft[First@#, Abs@Last@# + Length@First@#]&@RealDigits[N[1/333, 100]] (* _Vincenzo Librandi_, Jun 22 2016 *)

%t PadRight[{}, 100, {0, 0, 3}] (* _Wesley Ivan Hurt_, Jul 02 2016 *)

%o (Magma) &cat [[0, 0, 3]^^30]; // _Wesley Ivan Hurt_, Jul 02 2016

%K nonn,cons,easy

%O 0,3

%A _N. J. A. Sloane_