A110568 Period 6: repeat [1, 0, 2, 2, 0, 1].

1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2

Offset: 0

Author

Paul Barry, Jul 27 2005

Keywords

• easy
• nonn

Comments

Permutation of {0, 1, 2}, followed by its reversal, repeated.

Links

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

Crossrefs

Cf. A078008, A088689, A105198, A110549, A110550, A110551, A110569.

Programs

Magma

&cat [[1, 0, 2, 2, 0, 1]^^30]; // Wesley Ivan Hurt, Jun 28 2016

Maple

A110568:=n->[1, 0, 2, 2, 0, 1][(n mod 6)+1]: seq(A110568(n), n=0..100); # Wesley Ivan Hurt, Jun 28 2016

Mathematica

Mod[#,3]&/@CoefficientList[Series[(1-x)/(1-x-2x^2),{x,0,100}],x] (* Harvey P. Dale, Mar 30 2011 *)
PadRight[{}, 100, {1, 0, 2, 2, 0, 1}] (* Wesley Ivan Hurt, Jun 28 2016 *)
LinearRecurrence[{1,-1,1,-1,1},{1,0,2,2,0},100] (* Harvey P. Dale, Apr 03 2019 *)

PARI

x='x+O('x^50); Vec((1-x+3*x^2-x^3+x^4)/(1-x+x^2-x^3+x^4-x^5)) \\ G. C. Greubel, Aug 31 2017

Formula

a(n) = A078008(n) mod 3.

G.f.: (1-x+3*x^2-x^3+x^4) / (1-x+x^2-x^3+x^4-x^5).

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.

a(n) = 1 + cos(2*Pi*n/3)/2 - sqrt(3)*sin(2*Pi*n/3)/2 - cos(Pi*n/3)/2 + sqrt(3)*sin(Pi*n/3)/6.

a(n) = a(n-6) for n > 5. - Wesley Ivan Hurt, Jun 28 2016

a(n) = ((n-1)*(-1)^(n-1) mod 3). - Wesley Ivan Hurt, Jan 07 2021

Extensions

Name changed by Wesley Ivan Hurt, Jun 28 2016