A070342 a(n) = 3^n mod 19.

1, 3, 9, 8, 5, 15, 7, 2, 6, 18, 16, 10, 11, 14, 4, 12, 17, 13, 1, 3, 9, 8, 5, 15, 7, 2, 6, 18, 16, 10, 11, 14, 4, 12, 17, 13, 1, 3, 9, 8, 5, 15, 7, 2, 6, 18, 16, 10, 11, 14, 4, 12, 17, 13, 1, 3, 9, 8, 5, 15, 7, 2, 6, 18, 16, 10, 11, 14, 4, 12, 17, 13, 1, 3, 9

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Links

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

Programs

Mathematica

PowerMod[3, Range[0, 50], 19] (* G. C. Greubel, Mar 12 2016 *)

PARI

a(n)=lift(Mod(3,19)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(3,n,19)for n in range(0, 75)] # Zerinvary Lajos, Nov 25 2009

Formula

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

a(n)= a(n-1) - a(n-9) + a(n-10).

G.f.: (1+2*x+6*x^2-x^3-3*x^4+10*x^5-8*x^6-5*x^7+4*x^8+13*x^9)/ ((1-x) * (1+x) * (x^2 -x+1) * (x^6-x^3+1)). (End)

a(n) = a(n-18). - G. C. Greubel, Mar 12 2016