OFFSET
0,6
COMMENTS
Period 6: repeat [1, 1, 1, 0, 1, 2]. - Joerg Arndt, Jun 09 2013
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1).
FORMULA
G.f.: ( -1-x^2-2*x^4+x^3 ) / ( (x-1)*(1-x+x^2)*(1+x+x^2) ). - R. J. Mathar, Jun 09 2013
a(n) = (n + 3) mod (2 + n mod 2) - Wesley Ivan Hurt, Aug 16 2014
From Wesley Ivan Hurt, Jun 23 2016: (Start)
a(n) = cos(n*Pi/6) * (6*cos(n*Pi/6)-3*cos(n*Pi/2)-sqrt(3)*sin(n*Pi/2))/3.
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5).
a(n) = a(n-6) for n>5. (End)
E.g.f.: cosh(x) - cosh(x/2)*sin(sqrt(3)*x/2)/sqrt(3) + cos(sqrt(3)*x/2)*sinh(x/2) + sinh(x). - Stefano Spezia, Jul 26 2024
MAPLE
MATHEMATICA
Table[Mod[n + 3, 2 + Mod[n, 2]], {n, 0, 100}] (* Wesley Ivan Hurt, Aug 16 2014 *)
LinearRecurrence[{1, -1, 1, -1, 1}, {1, 1, 1, 0, 1}, 120] (* Harvey P. Dale, Jan 17 2021 *)
PROG
(Magma) &cat [[1, 1, 1, 0, 1, 2]^^20]; // Wesley Ivan Hurt, Jun 23 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Apr 12 2004
STATUS
approved