A132954 Period 6: repeat [1, 2, 4, -1, -2, -4].

1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, -4, 1, 2

Offset: 0

Author

Paul Curtz, Nov 19 2007

Keywords

• sign
• easy

Comments

Nonsimple continued fraction expansion of (5+sqrt(13))/6 = 1.434258545... - R. J. Mathar, Mar 08 2012

Links

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

Programs

Magma

&cat [[1, 2, 4, -1, -2, -4]^^20]; // Wesley Ivan Hurt, Jun 20 2016

Maple

A132954:=n->[1, 2, 4, -1, -2, -4][(n mod 6)+1]: seq(A132954(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016

Mathematica

PadRight[{}, 100, {1, 2, 4, -1, -2, -4}] (* Wesley Ivan Hurt, Jun 20 2016 *)

PARI

a(n)=(2^n%7)*(-1)^(n%6>2) \\ Jaume Oliver Lafont, Mar 24 2009

Formula

a(n) = -a(n-3) for n>2. G.f.: (1+2*x+4*x^2)/((1+x)*(x^2-x+1)). [R. J. Mathar, Apr 13 2010]

a(n) = cos(n*Pi) + 2*sqrt(3)*sin(n*Pi/3). - Wesley Ivan Hurt, Jun 20 2016