OFFSET
0,3
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).
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
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 27 2005
EXTENSIONS
Name changed by Wesley Ivan Hurt, Jun 28 2016
STATUS
approved