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%I #61 Dec 14 2023 05:23:21
%S 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 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 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 Periodic with period 3: a(3n)=3, a(3n+1)=a(3n+2)=2.
%C Continued fraction expansion of (15 + sqrt(365))/10 = A176979. - _Klaus Brockhaus_, Apr 30 2010
%C First differences of A047390. - _Tom Edgar_, Jul 17 2014
%C Also decimal expansion of 322/999. - _Nicolas Bělohoubek_, Nov 11 2021
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=878">Encyclopedia of Combinatorial Structures 878</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F G.f.: (2*x^2 + 2*x + 3)/(1-x^3).
%F a(n) = Sum((1/3)*(2*alpha^2 + 3*alpha + 2)*alpha^(-1-n), where alpha = RootOf(-1+x^3)).
%F a(n) = ceiling(7*(n+1)/3) - ceiling(7*n/3). - _Tom Edgar_, Jul 17 2014
%F From _Nicolas Bělohoubek_, Nov 11 2021: (Start)
%F a(n) = 12/(a(n-2)*a(n-1)).
%F a(n) = 7 - a(n-2) - a(n-1). See also A069705 or A144437. (End)
%p spec := [S,{S=Union(Sequence(Z),Sequence(Z),Sequence(Prod(Z,Z,Z)))},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t PadRight[{},110,{3,2,2}] (* _Harvey P. Dale_, Mar 19 2013 *)
%t LinearRecurrence[{0, 0, 1},{3, 2, 2},105] (* _Ray Chandler_, Aug 25 2015 *)
%o (Haskell)
%o a052901 n = a052901_list !! n
%o a052901_list = cycle [3,2,2] -- _Reinhard Zumkeller_, Apr 08 2012
%o (PARI) Vec((2*x^2+2*x+3)/(1-x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Apr 08 2012
%Y Cf. A176979 (decimal expansion of (15+sqrt(365))/10).
%Y Cf. A208131 (partial products).
%K easy,nonn
%O 0,1
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _James A. Sellers_, Jun 06 2000
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