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%I #37 Dec 27 2023 08:37:26
%S 1,7,10,5,9,11,12,6,3,8,4,2,1,7,10,5,9,11,12,6,3,8,4,2,1,7,10,5,9,11,
%T 12,6,3,8,4,2,1,7,10,5,9,11,12,6,3,8,4,2,1,7,10,5,9,11,12,6,3,8,4,2,1,
%U 7,10,5,9,11,12,6,3,8,4,2,1,7,10,5,9,11,12,6,3,8,4,2,1,7,10,5,9,11,12
%N a(n) = 7^n mod 13.
%H G. C. Greubel, <a href="/A070405/b070405.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,-1,1).
%F From _R. J. Mathar_, Apr 20 2010: (Start)
%F a(n) = a(n-1) - a(n-6) + a(n-7).
%F G.f.: ( -1-6*x-3*x^2+5*x^3-4*x^4-2*x^5-2*x^6 ) / ( (x-1)*(x^2+1)*(x^4-x^2+1) ). (End)
%F a(n) = a(n-12). - _G. C. Greubel_, Mar 20 2016
%t PowerMod[7,Range[0,90],13] (* or *) LinearRecurrence[{1,0,0,0,0,-1,1},{1,7,10,5,9,11,12},100] (* _Harvey P. Dale_, May 20 2014 *)
%o (Sage) [power_mod(7,n,13) for n in range(0,91)] # _Zerinvary Lajos_, Nov 03 2009
%o (PARI) a(n) = lift(Mod(7, 13)^n); \\ _Altug Alkan_, Mar 20 2016
%o (Magma) [Modexp(7, n, 13): n in [0..100]]; // _Bruno Berselli_, Mar 22 2016
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
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