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a(n) = n^3 mod 14.
1

%I #21 Dec 18 2023 14:43:04

%S 0,1,8,13,8,13,6,7,8,1,6,1,6,13,0,1,8,13,8,13,6,7,8,1,6,1,6,13,0,1,8,

%T 13,8,13,6,7,8,1,6,1,6,13,0,1,8,13,8,13,6,7,8,1,6,1,6,13,0,1,8,13,8,

%U 13,6,7,8,1,6,1,6,13,0,1,8,13,8,13,6,7,8,1,6,1,6,13,0,1,8,13,8,13,6,7,8,1

%N a(n) = n^3 mod 14.

%H G. C. Greubel, <a href="/A070476/b070476.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%F From _G. C. Greubel_, Mar 28 2016: (Start)

%F a(n) = a(n-14).

%F G.f.: (-x -8*x^2 -13*x^3 -8*x^4 -13*x^5 -6*x^6 -7*x^7 -8*x^8 -x^9 -6*x^10 -x^11 -6*x^12 -13*x^13)/(-1 + x^14). (End)

%t PowerMod[Range[0,100],3,14] (* _Harvey P. Dale_, Aug 23 2013 *)

%o (Sage) [power_mod(n,3,14 )for n in range(0, 94)] # _Zerinvary Lajos_, Oct 29 2009

%o (PARI) x='x+O('x^99); concat(0, Vec((-x-8*x^2-13*x^3-8*x^4-13*x^5-6*x^6 -7*x^7-8*x^8-x^9-6*x^10-x^11-6*x^12-13*x^13)/(-1+x^14))) \\ _Altug Alkan_, Mar 28 2016

%K nonn

%O 0,3

%A _N. J. A. Sloane_, May 12 2002