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A110568 Period 6: repeat [1, 0, 2, 2, 0, 1]. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..92.

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

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) = (1/30)*{2*[n mod 6]-3*[(n+1) mod 6]+12*[(n+2) mod 6]+2*[(n+3) mod 6]-8*[(n+4) mod 6]+7*[(n+5) mod 6]}. - Paolo P. Lava, Jun 01 2007

a(n) = a(n-6) for n>5. - 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 *)

PROG

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

(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

CROSSREFS

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

Sequence in context: A004594 A124210 A287447 * A088689 A076898 A174294

Adjacent sequences:  A110565 A110566 A110567 * A110569 A110570 A110571

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 27 2005

EXTENSIONS

Name changed by Wesley Ivan Hurt, Jun 28 2016

STATUS

approved

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Last modified March 30 09:35 EDT 2020. Contains 333125 sequences. (Running on oeis4.)