A132367 Period 6: repeat [1, 1, 2, -1, -1, -2].

1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2, 1, 1, 2, -1, -1, -2

Offset: 0

Author

Paul Curtz, Nov 09 2007

Keywords

• sign
• easy
• less

Comments

Nonsimple continued fraction expansion of 1+1/sqrt(3) = 1 + A020760. - R. J. Mathar, Mar 08 2012

Links

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

Crossrefs

Cf. A020760, A061347, A100051, A100063, A122876.

Programs

Magma

&cat[[1, 1, 2, -1, -1, -2]^^20]; // Wesley Ivan Hurt, Jun 19 2016

Maple

A132367:=n->[1, 1, 2, -1, -1, -2][(n mod 6)+1]: seq(A132367(n), n=0..100); # Wesley Ivan Hurt, Jun 19 2016

Mathematica

PadRight[{}, 120, {1,1,2,-1,-1,-2}] (* Harvey P. Dale, Jul 28 2012 *)

PARI

a(n)=[1,1,2,-1,-1,-2][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

Formula

a(n) = cos(Pi*n/3)/3+sqrt(3)*sin(Pi*n/3)+2*(-1)^n/3. - R. J. Mathar, Oct 08 2011

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

G.f.: (1+x+2*x^2)/(1+x^3).

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