A070353 a(n) = 3^n mod 14.

1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5, 1, 3, 9, 13, 11, 5

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

Formula

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

a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3).

G.f.: (1+x+5*x^2) / ((1-x)*(x^2-x+1)). (End)

E.g.f.: 7*exp(x) - (2/sqrt(3))*exp(x/2)*sin(sqrt(3)*x/2) - 6*exp(x/2)*cos(sqrt(3)*x/2). - G. C. Greubel, Mar 11 2016

Mathematica

PowerMod[3, Range[0, 90], 14] (* or *) LinearRecurrence[{2, -2, 1}, {1, 3, 9}, 90] (* Harvey P. Dale, Jul 12 2014 *)

Prog

(Sage) [power_mod(3, n, 14) for n in range(0, 90)] # Zerinvary Lajos, Nov 24 2009
(PARI) a(n)=lift(Mod(3, 14)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 14): n in [0..100]]; // Bruno Berselli, Mar 23 2016

Crossrefs

Sequence in context: A045769 A262539 A101537 * A029458 A050571 A234286

Adjacent sequences: A070350 A070351 A070352 * A070354 A070355 A070356

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved