A131716 Period 6: repeat [0, 1, 2, 5, 8, 9].

0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1, 2, 5, 8, 9, 0, 1

Offset: 0

Author

Paul Curtz, Sep 14 2007

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A131711.

Programs

Magma

&cat[[0, 1, 2, 5, 8, 9]^^20]; // Wesley Ivan Hurt, Jun 19 2016

Maple

A131716:=n->[0, 1, 2, 5, 8, 9][(n mod 6)+1]: seq(A131716(n), n=0..100); # Wesley Ivan Hurt, Jun 19 2016

Mathematica

PadRight[{}, 200, {0, 1, 2, 5, 8, 9}] (* Wesley Ivan Hurt, Jun 19 2016 *)

Formula

From Wesley Ivan Hurt, Jun 19 2016: (Start)

G.f.: x*(1+2*x+5*x^2+8*x^3+9*x^4)/(1-x^6).

a(n) = a(n-6) for n>5.

a(n) = (25 - 5*cos(n*Pi) - 10*cos(n*Pi/3) - 10*cos(2*n*Pi/3) - 14*sqrt(3)*sin(n*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3))/6. (End)