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.
%I A172162 #18 Apr 25 2022 08:01:50
%S A172162 0,1,101,10201,1020401,102050701,10205121101,1020513261601,
%T A172162 102051333512201,10205133479922901,1020513348977553701,
%U A172162 102051334912467474601,10205133491373712765601,1020513349139081705516701,102051334913924160974827901,10205133491392617410795809201
%N A172162 a(n) = ( A165154(n) + A165155(n) )/2.
%H A172162 Colin Barker, <a href="/A172162/b172162.txt">Table of n, a(n) for n = 0..500</a>
%H A172162 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (102,-101,-9900).
%F A172162 a(n) = 99*100^n/9701 - 11^n/178 - (-9)^n/218. [_Bruno Berselli_, Oct 02 2015]
%F A172162 From _Colin Barker_, Oct 02 2015: (Start)
%F A172162 a(n) = 102*a(n-1) - 101*a(n-2) - 9900*a(n-3) for n>3.
%F A172162 G.f.: x*(1-x) / ((1+9*x)*(1-11*x)*(1-100*x)).
%F A172162 (End)
%t A172162 Table[99 100^n/9701 - 11^n/178 - (-9)^n/218, {n, 0, 20}] (* _Bruno Berselli_, Oct 02 2015 *)
%o A172162 (PARI) concat(0, Vec(-x*(x-1)/((9*x+1)*(11*x-1)*(100*x-1)) + O(x^30))) \\ _Colin Barker_, Oct 02 2015
%o A172162 (SageMath) [(-89*(-9)^n - 109*11^n + 198*10^(2*n))/19402 for n in (0..50)] # _G. C. Greubel_, Apr 24 2022
%Y A172162 Cf. A162741, A162849, A165154, A165155, A172163.
%K A172162 nonn,easy
%O A172162 0,3
%A A172162 _Mark Dols_, Jan 27 2010
%E A172162 a(0) and more terms added by _Bruno Berselli_, Oct 02 2015