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A130784 Period 3: repeat [1, 3, 2].

%I A130784 #63 Dec 14 2023 05:21:13
%S A130784 1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,
%T A130784 3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,
%U A130784 2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3
%N A130784 Period 3: repeat [1, 3, 2].
%C A130784 Continued fraction expansion of (3+sqrt(37))/7 (A176977). - _Klaus Brockhaus_, Apr 30 2010
%C A130784 Pairwise sums of A010872(n). - _Wesley Ivan Hurt_, Jul 08 2014
%C A130784 Decimal expansion of 44/333. - _David A. Corneth_, Jul 02 2016
%H A130784 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A130784 a(n) = 4 - n + 3*floor((n-1)/3). - _Wesley Ivan Hurt_, Nov 30 2013
%F A130784 a(n) = A080425(n) + 1. - _Wesley Ivan Hurt_, Jul 08 2014
%F A130784 a(n) = 3 - ((n+5) mod 3) = 1 + (-n mod 3). - _Wesley Ivan Hurt_, Aug 29 2014
%F A130784 From _Robert Israel_, Aug 29 2014: (Start)
%F A130784 a(n) = 3*a(n-1)^2/2 - 13*a(n-1)/2 + 8.
%F A130784 O.g.f.: (1+z)*(1+2*z)/(1-z^3).
%F A130784 E.g.f.: 2*exp(z) - 2/sqrt(3)*exp(-z/2)*cos(sqrt(3)*z/2+Pi/6). (End)
%F A130784 a(n) = a(n-3) for n>2. - _Wesley Ivan Hurt_, Jul 02 2016
%p A130784 A130784:=n->4-n+3*floor((n-1)/3); seq(A130784(n), n=0..100); # _Wesley Ivan Hurt_, Nov 30 2013
%t A130784 PadRight[{}, 111, {1,3,2}] (* _Harvey P. Dale_, Apr 20 2012 *)
%t A130784 CoefficientList[Series[(1 + 3 x + 2 x^2)/(1 - x^3), {x, 0, 120}], x] (* _Michael De Vlieger_, Jul 02 2016 *)
%o A130784 (PARI) a(n)=[1,3,2][n%3+1] \\ _Charles R Greathouse IV_, Jun 02 2011
%o A130784 (Magma) [(n mod 3) + ((n+1) mod 3) : n in [0..100]]; // _Wesley Ivan Hurt_, Jul 08 2014
%Y A130784 Cf. A010872, A080425, A176977.
%K A130784 nonn,easy
%O A130784 0,2
%A A130784 _Paul Curtz_, Jul 15 2007