A168430 a(n) = 4^n mod 13.

1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10, 1, 4, 3, 12, 9, 10

Offset: 0

Author

Zerinvary Lajos, Nov 25 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 1).

Programs

Magma

[Modexp(4, n, 13): n in [0..100]]; // Vincenzo Librandi, Jul 23 2016

Magma

&cat[[1,4, 3,12,9,10]^^20]; // Vincenzo Librandi, Jul 23 2016

Mathematica

PowerMod[4,Range[0,100],13] (* or *) PadRight[{},100,{1,4,3,12,9,10}] (* Harvey P. Dale, Mar 15 2015 *)

PARI

a(n)=lift(Mod(4,13)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(4, n, 13)for n in range(0, 90)]

Formula

From R. J. Mathar, Apr 13 2010: (Start)

a(n) = a(n-1) - a(n-3) + a(n-4).

G.f.: (1 + 3*x - x^2 + 10*x^3)/ ((1-x) * (1+x) * (x^2-x+1)). (End)

From Wesley Ivan Hurt, Sep 08 2022: (Start)

a(n) = (39-13*(-1)^n-20*cos(n*Pi/3)-12*sqrt(3)*sin(n*Pi/3))/6.

a(n) = a(n-6) for n >= 6. (End)