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a(n) = n^6 mod 36.
0

%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