A122876 -id:A122876 - cp's OEIS frontend

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

Paul Curtz, Nov 09 2007

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

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

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

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

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

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

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

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)

A177702 Period 3: repeat [1, 1, 2].

Original entry on oeis.org

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

Klaus Brockhaus, May 11 2010

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)|.

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

Cf. A022003, A131534, A177703.

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

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

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

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

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

cp's OEIS Frontend

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

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