OFFSET
0,3
COMMENTS
a(m*n) = a(m)*a(n) mod 6; a(3*n+k) = a(3*n-k) for k <= 3*n. - Reinhard Zumkeller, Apr 24 2009
Equivalently n^6 mod 6. - Zerinvary Lajos, Nov 06 2009
Equivalently: n^(2*m + 4) mod 6; n^(2*m + 2) mod 6. - G. C. Greubel, Apr 01 2016
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1).
FORMULA
G.f.: -x*(1+4*x+3*x^2+4*x^3+x^4)/((x-1)*(1+x)*(1+x+x^2)*(x^2-x+1)). - R. J. Mathar, Jul 23 2009
a(n) = a(n-6). - Reinhard Zumkeller, Apr 24 2009
From G. C. Greubel, Apr 01 2016: (Start)
a(6*m) = 0.
a(2*n) = 4*A011655(n).
a(n) = (1/6)*(13 + 3*(-1)^n - 12*cos(n*Pi/3) - 4*cos(2*n*Pi/3)).
G.f.: (x +4*x^2 +3*x^3 + 4*x^4 +x^5)/(1 - x^6). (End)
MAPLE
MATHEMATICA
Table[Mod[n^2, 6], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1}, {0, 1, 4, 3, 4, 1}, 101] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0, 120], 2, 6] (* or *) PadRight[{}, 120, {0, 1, 4, 3, 4, 1}] (* Harvey P. Dale, Aug 11 2019 *)
PROG
(Sage) [power_mod(n, 2, 6) for n in range(0, 101)] # Zerinvary Lajos, Oct 30 2009
(PARI) a(n)=n^2%6 \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [n^2 mod 6 : n in [0..100]]; // Wesley Ivan Hurt, Apr 01 2016
(Magma) [Modexp(n, 2, 6): n in [0..100]]; // Vincenzo Librandi, Apr 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 12 2002
STATUS
approved