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A052901 Periodic with period 3: a(3n)=3, a(3n+1)=a(3n+2)=2. 5
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Continued fraction expansion of (15 + sqrt(365))/10. - Klaus Brockhaus, Apr 30 2010

First differences of A047390. - Tom Edgar, Jul 17 2014

LINKS

Table of n, a(n) for n=0..104.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 878

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1).

FORMULA

G.f.: (2*x^2 + 2*x + 3)/(1-x^3).

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

From Paolo P. Lava, Nov 21 2006: (Start)

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

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

a(n) = ceiling(7*(n+1)/3) - ceiling(7*n/3). - Tom Edgar, Jul 17 2014

MAPLE

spec := [S, {S=Union(Sequence(Z), Sequence(Z), Sequence(Prod(Z, Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

MATHEMATICA

PadRight[{}, 110, {3, 2, 2}] (* Harvey P. Dale, Mar 19 2013 *)

LinearRecurrence[{0, 0, 1}, {3, 2, 2}, 105] (* Ray Chandler, Aug 25 2015 *)

PROG

(Haskell)

a052901 n = a052901_list !! n

a052901_list = cycle [3, 2, 2]  -- Reinhard Zumkeller, Apr 08 2012

(PARI) Vec((2*x^2+2*x+3)/(1-x^3)+O(x^99)) \\ Charles R Greathouse IV, Apr 08 2012

CROSSREFS

Cf. A176979 (decimal expansion of (15+sqrt(365))/10).

Cf. A208131 (partial products).

Sequence in context: A178086 A281977 A240666 * A127807 A122028 A245070

Adjacent sequences:  A052898 A052899 A052900 * A052902 A052903 A052904

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

More terms from James A. Sellers, Jun 06 2000

STATUS

approved

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Last modified October 20 08:05 EDT 2019. Contains 328252 sequences. (Running on oeis4.)