A154595 Period 6: repeat [1, 3, 3, -1, -3, -3].

1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3, 3, -1, -3, -3, 1, 3

Offset: 0

Author

Paul Curtz, Jan 12 2009

Keywords

• sign
• easy

Comments

First differences of A154127.

Links

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

Crossrefs

Cf. A154127.

Programs

Magma

&cat [[1, 3, 3, -1, -3, -3]^^20]; // Wesley Ivan Hurt, Jun 23 2016

Maple

A154595:=n->[1, 3, 3, -1, -3, -3][(n mod 6)+1]: seq(A154595(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

Mathematica

PadRight[{}, 120, {1,3,3,-1,-3,-3}] (* Harvey P. Dale, Aug 09 2013 *)

Formula

G.f.: ( 1+3*x+3*x^2 ) / ( (1+x)*(x^2-x+1) ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Jun 23 2016: (Start)

a(n) + a(n-3) = 0 for n>2.

a(n) = (cos(n*Pi) + 2*cos(n*Pi/3) + 6*sqrt(3)*sin(n*Pi/3))/3. (End)

Extensions

Edited by N. J. A. Sloane, Jan 12 2009