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A052901 Periodic with period 3: a(3n)=3, a(3n+1)=a(3n+2)=2. 5

%I

%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. - _Klaus Brockhaus_, Apr 30 2010

%C First differences of A047390. - _Tom Edgar_, Jul 17 2014

%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 Sum((1/3)*(2*alpha^2 + 3*alpha + 2)*alpha^(-1-n), where alpha = RootOf(-1+x^3)).

%F From _Paolo P. Lava_, Nov 21 2006: (Start)

%F a(n) = 2 + (2/3)*(cos(n*Pi*2/3) + 1/2);

%F a(n) = (1/9)*(4*(n mod 3) + 7*((n+1) mod 3) + 10*((n+2) mod 3)). (End)

%F a(n) = ceiling(7*(n+1)/3) - ceiling(7*n/3). - _Tom Edgar_, Jul 17 2014

%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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Last modified August 19 20:20 EDT 2019. Contains 326133 sequences. (Running on oeis4.)