A110569 Period 6: repeat [2, 1, 3, 3, 1, 2].

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

Offset: 0

Author

Paul Barry, Jul 27 2005

Keywords

• easy
• nonn

Comments

Permutation of {1, 2, 3}, followed by its reversal, repeated.

Links

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

Crossrefs

Cf. A078008, A105198, A110549, A110550, A110551, A110568.

Programs

Magma

&cat [[2, 1, 3, 3, 1, 2]^^30]; // Wesley Ivan Hurt, Jun 27 2016

Maple

A110569:=n->[2, 1, 3, 3, 1, 2][(n mod 6)+1]: seq(A110569(n), n=0..100); # Wesley Ivan Hurt, Jun 27 2016

Mathematica

PadRight[{}, 100, {2, 1, 3, 3, 1, 2}] (* Wesley Ivan Hurt, Jun 27 2016 *)

PARI

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

Formula

a(n) = 1+(A078008(n) mod 3).

G.f.: (2-x+4*x^2-x^3+2*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) = 2 + 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 27 2016

Extensions

Name changed by Wesley Ivan Hurt, Jun 27 2016