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A052901 Periodic with period 3: a(3n)=3, a(3n+1)=a(3n+2)=2.

%I A052901 #62 Jul 02 2025 16:01:58
%S A052901 3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,
%T A052901 2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,
%U A052901 2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2,3,2,2
%N A052901 Periodic with period 3: a(3n)=3, a(3n+1)=a(3n+2)=2.
%C A052901 Continued fraction expansion of (15 + sqrt(365))/10 = A176979. - _Klaus Brockhaus_, Apr 30 2010
%C A052901 First differences of A047390. - _Tom Edgar_, Jul 17 2014
%C A052901 Also decimal expansion of 322/999. - _Nicolas Bělohoubek_, Nov 11 2021
%H A052901 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=878">Encyclopedia of Combinatorial Structures 878</a>
%H A052901 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A052901 G.f.: (2*x^2 + 2*x + 3)/(1-x^3).
%F A052901 a(n) = Sum((1/3)*(2*alpha^2 + 3*alpha + 2)*alpha^(-1-n), where alpha = RootOf(-1+x^3)).
%F A052901 a(n) = ceiling(7*(n+1)/3) - ceiling(7*n/3). - _Tom Edgar_, Jul 17 2014
%F A052901 From _Nicolas Bělohoubek_, Nov 11 2021: (Start)
%F A052901 a(n) = 12/(a(n-2)*a(n-1)).
%F A052901 a(n) = 7 - a(n-2) - a(n-1). See also A069705 or A144437. (End)
%p A052901 spec := [S,{S=Union(Sequence(Z),Sequence(Z),Sequence(Prod(Z,Z,Z)))},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052901 PadRight[{},110,{3,2,2}] (* _Harvey P. Dale_, Mar 19 2013 *)
%t A052901 LinearRecurrence[{0, 0, 1},{3, 2, 2},105] (* _Ray Chandler_, Aug 25 2015 *)
%o A052901 (Haskell)
%o A052901 a052901 n = a052901_list !! n
%o A052901 a052901_list = cycle [3,2,2]  -- _Reinhard Zumkeller_, Apr 08 2012
%o A052901 (PARI) Vec((2*x^2+2*x+3)/(1-x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Apr 08 2012
%Y A052901 Cf. A176979 (decimal expansion of (15+sqrt(365))/10).
%Y A052901 Cf. A208131 (partial products).
%K A052901 easy,nonn
%O A052901 0,1
%A A052901 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052901 More terms from _James Sellers_, Jun 06 2000