A177702 Period 3: 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

Klaus Brockhaus, May 11 2010

Keywords

• cofr
• nonn
• easy

Comments

Continued fraction expansion of (2+sqrt(10))/3.

Decimal expansion of 112/999.

a(n) = A131534(n+2) = |A132419(n)| = |A132367(n)| = |A131556(n+2)|= |A122876(n)|.

Links

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

Crossrefs

Cf. A022003, A131534, A177703.

Programs

Magma

&cat[ [1, 1, 2]: k in [1..35] ];

Maple

seq(op([1, 1, 2]), n=1..50); # Wesley Ivan Hurt, Jul 01 2016

Mathematica

PadRight[{},120,{1,1,2}] (* or *) LinearRecurrence[{0,0,1},{1,1,2},120] (* Harvey P. Dale, Dec 19 2014 *)

PARI

a(n)=max(n%3,1) \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = a(n-3) for n > 2, with a(0) = 1, a(1) = 1, a(2) = 2.

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

a(n) = 4/3 - cos(2*Pi*n/3)/3 - sin(2*Pi*n/3)/sqrt(3). - R. J. Mathar, Oct 08 2011

a(n) = 1 + A022003(n). - Wesley Ivan Hurt, Jul 01 2016