A158677 Period 6: repeat [3, 4, 0, 5, 6, 3].

3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0

Offset

1,1

Comments

Also the decimal expansion of 1135210/333333 or the continued fraction of (81+sqrt(9867))/58.

Links

Table of n, a(n) for n=1..105.

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

Formula

G.f.: x*(3+4*x+5*x^3+6*x^4+3*x^5) / ((1-x)*(1+x)*(1+x+x^2)*(x^2-x+1)).

a(n) = a(n-6) for n>6.

a(n) = cos(n*Pi/6)^2 * (39 - 36*cos(n*Pi/3) + 6*cos(2*n*Pi/3) - 4*sqrt(3)*sin(n*Pi/3))/3. - Wesley Ivan Hurt, Jun 23 2016

Maple

A158677:=n->[3, 4, 0, 5, 6, 3][(n mod 6)+1]: seq(A158677(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

Mathematica

PadRight[{}, 120, {3, 4, 0, 5, 6, 3}] (* Harvey P. Dale, Aug 06 2013 *)

Prog

(Magma) &cat [[3, 4, 0, 5, 6, 3]^^20]; // Wesley Ivan Hurt, Jun 23 2016

Crossrefs

Cf. A158674.

Sequence in context: A197809 A086230 A197485 * A337164 A105576 A105826

Adjacent sequences: A158674 A158675 A158676 * A158678 A158679 A158680

Keyword

nonn,easy

Author

Paul Curtz, Mar 24 2009

Extensions

Edited and extended by R. J. Mathar, Sep 07 2009

Status

approved