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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
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)
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) = 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: A334337 A370562 A205449 * A183164 A364490 A019762
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