%I #30 Dec 25 2023 13:46:51
%S 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,
%T 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,
%U 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
%N a(n) = 3^n mod 14.
%H G. C. Greubel, <a href="/A070353/b070353.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,1).
%F From _R. J. Mathar_, Apr 13 2010: (Start)
%F a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3).
%F G.f.: (1+x+5*x^2) / ((1-x)*(x^2-x+1)). (End)
%F 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
%t PowerMod[3,Range[0,90],14] (* or *) LinearRecurrence[{2,-2,1},{1,3,9},90] (* _Harvey P. Dale_, Jul 12 2014 *)
%o (Sage) [power_mod(3, n, 14) for n in range(0, 90)] # _Zerinvary Lajos_, Nov 24 2009
%o (PARI) a(n)=lift(Mod(3,14)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o (Magma) [Modexp(3, n, 14): n in [0..100]]; // _Bruno Berselli_, Mar 23 2016
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 12 2002