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a(n) = n^3 mod 18.
1

%I #24 Dec 18 2023 14:45:53

%S 0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,10,

%T 17,0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,

%U 10,17,0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,10,17,0,1,8,9,10,17

%N a(n) = n^3 mod 18.

%H G. C. Greubel, <a href="/A070480/b070480.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 1).

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

%F a(n) = a(n-6).

%F G.f.: (-x -8*x^2 -9*x^3 -10*x^4 -17*x^5)/(-1 + x^6). (End)

%t Table[Mod[n^3, 18], {n, 0, 100}] (* _G. C. Greubel_, Mar 28 2016 *)

%o (Sage) [power_mod(n,3,18 )for n in range(0, 90)] # _Zerinvary Lajos_, Oct 29 2009

%o (Magma) [Modexp(n, 3, 18): n in [0..100]]; // _Vincenzo Librandi_, Mar 28 2016

%o (PARI) x='x+O('x^99); concat(0, Vec((-x-8*x^2-9*x^3-10*x^4-17*x^5) / (-1+x^6))) \\ _Altug Alkan_, Mar 28 2016

%K nonn,easy

%O 0,3

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