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A130196 Period 3: repeat [1, 2, 2].

%I A130196 #62 Apr 12 2025 18:29:11
%S A130196 1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,
%T A130196 2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,
%U A130196 2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2,1,2,2
%N A130196 Period 3: repeat [1, 2, 2].
%C A130196 From _Reinhard Zumkeller_, Nov 12 2009: (Start)
%C A130196 Denominator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/2; numerator = A167808;
%C A130196 a(n) = A131534(n) + A022003(n) = A080425(n) - A131534(n) + 2 = A153727(n)/A131534(n). (End)
%C A130196 Continued fraction expansion of (5+sqrt(85))/10. - _Klaus Brockhaus_, May 07 2010
%H A130196 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A130196 a(n+3) = a(n) with a(0)=1, a(1)=a(2)=2.
%F A130196 G.f.: (1+2*x+2*x^2)/(1-x)*(x^2+x+1). - _R. J. Mathar_, Nov 14 2007
%F A130196 a(n) = (5 - 2*cos(2*Pi*n/3))/3. - _Jaume Oliver Lafont_, Nov 23 2008
%F A130196 a(n) = 2 - 0^(n mod 3). - _Reinhard Zumkeller_, Nov 12 2009
%F A130196 a(n) = A011655(n) + 1 = (n^2 mod 3) + 1. - _Boris Putievskiy_, Feb 03 2013
%F A130196 a(n) = floor((n+1)*5/3) - floor(n*5/3). - _Hailey R. Olafson_, Jul 23 2014
%F A130196 E.g.f.: (5*exp(x) - 2*exp(-x/2)*cos(sqrt(3)*x/2))/3. - _Stefano Spezia_, Jun 03 2021
%p A130196 A130196:=n->floor(5*(n+1)/3)-floor(5*n/3): seq(A130196(n), n=0..100); # _Wesley Ivan Hurt_, Jul 24 2014
%t A130196 Table[Floor[5 (n + 1)/3] - Floor[5 n/3], {n, 0, 100}] (* _Wesley Ivan Hurt_, Jul 24 2014 *)
%t A130196 Denominator[LinearRecurrence[{1,1},{0,1/2},110]] (* or *) PadRight[{},110,{1,2,2}] (* _Harvey P. Dale_, Aug 08 2014 *)
%t A130196 LinearRecurrence[{0, 0, 1},{1, 2, 2},105] (* _Ray Chandler_, Aug 03 2015 *)
%o A130196 (PARI) a(n)=2-0^(n%3) \\ _Charles R Greathouse IV_, Jun 01 2011
%o A130196 (Magma) [Floor(5*(n+1)/3)-Floor(5*n/3) : n in [0..100]]; // _Wesley Ivan Hurt_, Jul 24 2014
%Y A130196 Cf. A177347 (decimal expansion of (5+sqrt(85))/10).
%Y A130196 Cf. A022003, A080425, A131534, A153727, A167808.
%K A130196 nonn,easy
%O A130196 0,2
%A A130196 _Paul Curtz_, Aug 05 2007
%E A130196 More terms from _Klaus Brockhaus_, May 07 2010