A177702 - OEIS

%I #26 Dec 12 2023 07:41:54

%S 1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,

%T 1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,

%U 2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2

%N Period 3: repeat [1, 1, 2].

%C Continued fraction expansion of (2+sqrt(10))/3.

%C Decimal expansion of 112/999.

%C a(n) = A131534(n+2) = |A132419(n)| = |A132367(n)| = |A131556(n+2)|= |A122876(n)|.

%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-3) for n > 2, with a(0) = 1, a(1) = 1, a(2) = 2.

%F G.f.: (1+x+2*x^2)/(1-x^3).

%F a(n) = 4/3 - cos(2*Pi*n/3)/3 - sin(2*Pi*n/3)/sqrt(3). - _R. J. Mathar_, Oct 08 2011

%F a(n) = 1 + A022003(n). - _Wesley Ivan Hurt_, Jul 01 2016

%p seq(op([1, 1, 2]), n=1..50); # _Wesley Ivan Hurt_, Jul 01 2016

%t PadRight[{},120,{1,1,2}] (* or *) LinearRecurrence[{0,0,1},{1,1,2},120] (* _Harvey P. Dale_, Dec 19 2014 *)

%o (Magma) &cat[ [1, 1, 2]: k in [1..35] ];

%o (PARI) a(n)=max(n%3,1) \\ _Charles R Greathouse IV_, Jul 17 2016

%Y Cf. A022003, A131534, A177703.

%K cofr,nonn,easy

%O 0,3

%A _Klaus Brockhaus_, May 11 2010