A132677 Period 3: repeat [1, 2, -3].

1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3, 1, 2, -3

Offset: 0

Author

Paul Curtz, Nov 15 2007

Keywords

• sign
• easy

Comments

a(n) is proportional to its 6n-th differences.

Nonsimple continued fraction expansion of 1+sqrt(2/5) = 1.63245553... (see A010494). - R. J. Mathar, Mar 08 2012

Links

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

Crossrefs

Cf. A000748, A010494, A049347, A101544.

Programs

Magma

&cat [[1, 2, -3]^^30]; // Wesley Ivan Hurt, Jul 01 2016

Maple

seq(op([1, 2, -3]), n=0..50); # Wesley Ivan Hurt, Jul 01 2016
A132677 := proc(n)
    op(1+modp(n,3),[1,2,-3]) ;
end proc: # R. J. Mathar, Mar 14 2025

Mathematica

PadRight[{}, 100, {1, 2, -3}] (* Wesley Ivan Hurt, Jul 01 2016 *)

PARI

a(n)=[1,2,-3][1+n%3] \\ Jaume Oliver Lafont, Mar 24 2009

Formula

G.f.: (1+3*x)/(1+x+x^2). - Jaume Oliver Lafont, Mar 24 2009

a(n) = cos(2*Pi*n/3) + 5*sin(2*Pi*n/3)/sqrt(3). - R. J. Mathar, Oct 08 2011

a(n) + a(n-1) + a(n-2) = 0 for n > 1, a(n) = a(n-3) for n > 2. - Wesley Ivan Hurt, Jul 01 2016