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A164360 Period 3: repeat [5, 4, 3]. 1
5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From Klaus Brockhaus, May 29 2010: (Start)

Continued fraction expansion of (32+sqrt(1297))/13.

Decimal expansion of 181/333. (End)

LINKS

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

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

FORMULA

a(n) = 4+(-1)^n*((1/2+I*sqrt(3)/6)*((1+I*sqrt(3))/2)^n+(1/2-I*sqrt(3)/6)*((1-I*sqrt(3))/2)^n). [Corrected by Klaus Brockhaus, Sep 17 2009]

a(n) = 4+(1/3)*sqrt(3)*sin(2*n*Pi/3)+cos(2*n*Pi/3). [Corrected by Klaus Brockhaus, Sep 17 2009]

a(n) = a(n-3) for n > 2, with a(0) = 5, a(1) = 4, a(2) = 3.

G.f.: (5+4*x+3*x^2)/((1-x)*(1+x+x^2)). [Klaus Brockhaus, Sep 17 2009]

E.g.f.: 4*exp(x)+(1/3)*sqrt(3)*exp(-(1/2)*x)*sin((1/2)*x*sqrt(3))+exp(-(1/2)*x)*cos((1/2)*x*sqrt(3)).

a(n) = (1/3)*(2*(n mod 3)+5*((n+1) mod 3)+5*((n+2) mod 3)). [Paolo P. Lava, Nov 12 2009]

a(n) = 4 + A057078(n). - Wesley Ivan Hurt, Jul 01 2016

MAPLE

seq(op([5, 4, 3]), n=0..50); # Wesley Ivan Hurt, Jul 01 2016

MATHEMATICA

PadRight[{}, 100, {5, 4, 3}] (* Wesley Ivan Hurt, Jul 01 2016 *)

PROG

(MAGMA) [ n le 3 select 6-n else Self(n-3):n in [1..105] ]; // Klaus Brockhaus, Sep 17 2009

(MAGMA) &cat [[5, 4, 3]^^30]; // Wesley Ivan Hurt, Jul 01 2016

CROSSREFS

Cf. A007877 (repeat 0,1,2,1), A068073 (repeat 1,2,3,2), A028356 (repeat 1,2,3,4,3,2), A130784 (repeat 1,3,2), A158289 (repeat 0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1).

Cf. A178566 (decimal expansion of (32+sqrt(1297))/13). [Klaus Brockhaus, May 29 2010]

Sequence in context: A061836 A021188 A205449 * A183164 A019762 A256099

Adjacent sequences:  A164357 A164358 A164359 * A164361 A164362 A164363

KEYWORD

easy,nonn

AUTHOR

Stephen Crowley, Aug 14 2009

EXTENSIONS

Edited by Klaus Brockhaus, Sep 17 2009

Offset changed to 0 and formulas adjusted by Klaus Brockhaus, May 18 2010

STATUS

approved

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Last modified July 22 16:43 EDT 2019. Contains 325225 sequences. (Running on oeis4.)