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

0,2

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).

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)

Mathematica

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

Prog

(Sage) [power_mod(4, n, 13)for n in range(0, 90)] #
(PARI) a(n)=lift(Mod(4, 13)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(4, n, 13): n in [0..100]]; /* or */ &cat[[1, 4, 3, 12, 9, 10]^^20]; // Vincenzo Librandi, Jul 23 2016

Crossrefs

Sequence in context: A271199 A055527 A055523 * A074324 A162766 A166552

Adjacent sequences: A168427 A168428 A168429 * A168431 A168432 A168433

Keyword

nonn,easy

Author

Zerinvary Lajos, Nov 25 2009

Status

approved