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A146325 Period 3: repeat [1, 4, 1].

%I A146325 #61 Dec 21 2023 17:00:22
%S A146325 1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,
%T A146325 4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,
%U A146325 1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1
%N A146325 Period 3: repeat [1, 4, 1].
%C A146325 Continued fraction of (1 + sqrt(26))/5 = A188659.
%C A146325 Digital roots of the centered triangular numbers A005448. - _Ant King_, May 08 2012
%C A146325 Also the digital roots of centered 12-gonal numbers A003154. - _Peter M. Chema_, Dec 20 2023
%H A146325 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A146325 a(n) = 4*(cos((2*n - 1)*Pi/3))^2 = 4 - 4*(sin((2*n - 1)*Pi/3))^2.
%F A146325 a(n+3) = a(n).
%F A146325 a(n) = 2 - cos(2*Pi*n/3) + sqrt(3)*sin(2*Pi*n/3).
%F A146325 O.g.f.: x*(1+4*x+x^2)/(1-x^3). [_Richard Choulet_, Nov 03 2008]
%F A146325 a(n) = 6 - a(n-1) - a(n-2) for n>2. - _Ant King_, Jun 12 2012
%F A146325 a(n) = (n mod 3)^(n mod 3). - _Bruno Berselli_, Jun 27 2016
%F A146325 a(n) = 1 + A021337(n) for n>0. - _Wesley Ivan Hurt_, Jul 01 2016
%p A146325 seq(op([1, 4, 1]), n=1..50); # _Wesley Ivan Hurt_, Jul 01 2016
%t A146325 Table[Round[N[4 (Cos[(2 n - 1) ArcTan[Sqrt[3]]])^2, 100]], {n, 1, 100}]
%t A146325 PadLeft[{},111,{1,4,1}] (* _Harvey P. Dale_, Sep 18 2011 *)
%o A146325 (PARI) a(n)=1+3*(n%3==2) \\ _Jaume Oliver Lafont_, Mar 24 2009
%o A146325 (Magma) &cat [[1,4,1]^^40]; // _Bruno Berselli_, Jun 27 2016
%Y A146325 Cf. A003154, A005448, A021337, A131534 (square roots), A188659.
%K A146325 nonn,easy
%O A146325 1,2
%A A146325 _Artur Jasinski_, Oct 30 2008