cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A039303 Number of distinct quadratic residues mod 6^n.

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%I A039303 #16 Sep 08 2022 08:44:53
%S A039303 1,4,8,33,124,644,3288,18883,108284,642234,3808768,22785833,136315044,
%T A039303 817291024,4900153448,29395534383,176340899404,1057996947014,
%U A039303 6347691029328,38085710240533,228511646005364,1371065953050204
%N A039303 Number of distinct quadratic residues mod 6^n.
%C A039303 Number of distinct n-digit suffixes of base-6 squares.
%H A039303 Vincenzo Librandi, <a href="/A039303/b039303.txt">Table of n, a(n) for n = 0..1000</a>
%F A039303 a(n+8) = 50 a(n+6) - 553 a(n+4) + 1800 a(n+2) - 1296 a(n) for n >= 1.
%F A039303 G.f.: (1 - 2*x - 30*x^2 + 13*x^3 + 199*x^4 + 12*x^5 - 360*x^6 - 108*x^7)/((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-3*x)*(1+3*x)*(1-6*x)). - _Colin Barker_, Mar 14 2012
%t A039303 CoefficientList[Series[(1-2*x-30*x^2+13*x^3+199*x^4+ 12*x^5-360*x^6-108*x^7)/((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-3*x)*(1+3*x)*(1-6*x)),{x,0,30}],x] (* _Vincenzo Librandi_, Apr 21 2012 *)
%o A039303 (Magma) I:=[1, 4, 8, 33, 124, 644, 3288, 18883, 108284]; [n le 9 select I[n] else 50*Self(n-2)-553*Self(n-4)+1800*Self(n-6)-1296*Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Apr 21 2012
%K A039303 nonn,easy
%O A039303 0,2
%A A039303 _David W. Wilson_