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A144110 Period 6: repeat [2, 2, 2, 1, 1, 1]. 1
2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = 2 for n = 0,1,2 modulo 6; a(n) = 1 for n = 3,4,5 modulo 6.

Terms of the simple continued fraction of 29/[2*sqrt(210)-17]. Decimal expansion of 667/3003. [Paolo P. Lava, Aug 05 2009]

LINKS

Table of n, a(n) for n=0..107.

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

FORMULA

G.f.: (1+2*x^3)/((1-x)*(1+x)*(1-x+x^2)); a(n) = 3/2-(-1)^n/6-A057079(n)/3. [R. J. Mathar, Sep 17 2008]

a(n) = (1/30)*{8*(n mod 6)+3*[(n+1) mod 6]+3*[(n+2) mod 6]-2*[(n+3) mod 6]+3*[(n+4) mod 6]+3*[(n+5) mod 6]}, with n>=0. [Paolo P. Lava, Sep 19 2008]

a(n) = a(n-1) - a(n-3) + a(n-4) for n>3; a(n) = 1 + mod(floor((-n-1)/3), 2); a(n) = A088911(n) + 1. - Wesley Ivan Hurt, Sep 04 2014

a(n) = (9 + cos(n*Pi) + 2*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/6. - Wesley Ivan Hurt, Jun 23 2016

MAPLE

A144110:=n->1+(floor((-n-1)/3) mod 2): seq(A144110(n), n=0..100); # Wesley Ivan Hurt, Sep 04 2014

MATHEMATICA

Table[1 + Mod[Floor[(-n - 1)/3], 2], {n, 0, 100}] (* Wesley Ivan Hurt, Sep 04 2014 *)

PROG

(MAGMA) [1+(Floor((-n-1)/3) mod 2) : n in [0..100]]; // Wesley Ivan Hurt, Sep 04 2014

(PARI) a(n)=[2, 2, 2, 1, 1, 1][n%6+1] \\ Edward Jiang, Sep 04 2014

CROSSREFS

Cf. A057079, A088911, A135265.

Sequence in context: A211226 A306366 A135265 * A076490 A320278 A302111

Adjacent sequences:  A144107 A144108 A144109 * A144111 A144112 A144113

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Sep 11 2008, Sep 15 2008

STATUS

approved

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Last modified September 28 07:46 EDT 2020. Contains 337394 sequences. (Running on oeis4.)