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 A225810 #25 Jul 05 2025 05:30:47
%S A225810 6,141,10401,1004001,100040001,10000400001,1000004000001,
%T A225810 100000040000001,10000000400000001,1000000004000000001,
%U A225810 100000000040000000001,10000000000400000000001,1000000000004000000000001,100000000000040000000000001,10000000000000400000000000001
%N A225810 a(n) = (10^n)^2 + 4*(10^n) + 1.
%C A225810 This is an instance of (10^n)^2 + x(10^n) + 1 which umbrellas A066138, A033934, A171375, A171410, A171461, A171513 and A171553 which all produce palindromes of the form 1...n...1 when n <> 0.
%H A225810 Colin Barker, <a href="/A225810/b225810.txt">Table of n, a(n) for n = 0..499</a>
%H A225810 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A225810 From _Colin Barker_, Apr 27 2015: (Start)
%F A225810 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3).
%F A225810 G.f.: -3*(470*x^2-175*x+2)/((x-1)*(10*x-1)*(100*x-1)). (End)
%F A225810 E.g.f.: exp(x)*(1 + 4*exp(9*x) + exp(99*x)). - _Elmo R. Oliveira_, Jul 04 2025
%t A225810 Table[(10^n)^2 + 4*(10^n) + 1, {n, 0, 20}] (* _T. D. Noe_, Aug 12 2013 *)
%t A225810 LinearRecurrence[{111,-1110,1000},{6,141,10401},20] (* _Harvey P. Dale_, Oct 28 2017 *)
%o A225810 (PARI) Vec(-3*(470*x^2-175*x+2)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100)) \\ _Colin Barker_, Apr 27 2015
%Y A225810 Cf. A033934, A066138, A171375, A171410, A171461, A171513, A171553.
%K A225810 nonn,easy
%O A225810 0,1
%A A225810 _Lance J. Weingartz_, Jul 29 2013