%I #16 Dec 26 2023 20:54:12
%S 0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,28,
%T 1,0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,
%U 28,1,0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,28,1,0,1,28,9,28,1
%N a(n) = n^6 mod 36.
%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 _Wesley Ivan Hurt_, Dec 26 2023: (Start)
%F a(n) = (67+45*(-1)^n-72*cos(n*Pi/3)-40*cos(2*Pi*n/3))/6.
%F G.f.: x*(1+28*x+9*x^2+28*x^3+x^4)/(1-x^6).
%F a(n) = a(n-6). (End)
%t PowerMod[Range[0, 100], 6, 36] (* _Wesley Ivan Hurt_, Dec 26 2023 *)
%o (Sage) [power_mod(n, 6, 36) for n in range(90)] # _Zerinvary Lajos_, Nov 07 2009
%o (PARI) a(n)=n^6%36 \\ _Charles R Greathouse IV_, Apr 06 2016
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 13 2002