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%I #24 Sep 08 2022 08:45:05
%S 0,1,4,9,16,3,14,5,20,15,12,11,12,15,20,5,14,3,16,9,4,1,0,1,4,9,16,3,
%T 14,5,20,15,12,11,12,15,20,5,14,3,16,9,4,1,0,1,4,9,16,3,14,5,20,15,12,
%U 11,12,15,20,5,14,3,16,9,4,1,0,1,4,9,16,3,14,5,20,15,12,11,12,15,20,5
%N a(n) = n^2 mod 22.
%H Vincenzo Librandi, <a href="/A070444/b070444.txt">Table of n, a(n) for n = 0..3000</a>
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F From _R. J. Mathar_, Jul 27 2015: (Start)
%F a(n) = a(n-22).
%F G.f.: -x*(1 +4*x +9*x^2 +16*x^3 +3*x^4 +14*x^5 +5*x^6 +20*x^7 +15*x^8 +12*x^9 +11*x^10 +12*x^11 +15*x^12 +20*x^13 +5*x^14 +14*x^15 +3*x^16 +16*x^17 +9*x^18 +4*x^19+x^20) ) / ( (x-1) *(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) *(1+x) *(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10) ). (End)
%t Table[Mod[n^2,22],{n,0,200}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 23 2011 *)
%t PowerMod[Range[0,120],2,22] (* or *) PadRight[{},120,{0,1,4,9,16,3,14,5,20,15,12,11,12,15,20,5,14,3,16,9,4,1}] (* _Harvey P. Dale_, May 28 2021 *)
%o (Maxima) makelist(power_mod (n, 2, 22), n, 0, 81); \\ _Bruno Berselli_, May 25 2011
%o (Magma) [n^2 mod (22): n in [0..80]]; // _Vincenzo Librandi_, May 26 2011
%o (PARI) a(n)=n^2%22 \\ _Charles R Greathouse IV_, Apr 06 2016
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 12 2002
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