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 A225813 #27 Jul 05 2025 05:31:02
%S A225813 9,171,10701,1007001,100070001,10000700001,1000007000001,
%T A225813 100000070000001,10000000700000001,1000000007000000001,
%U A225813 100000000070000000001,10000000000700000000001,1000000000007000000000001,100000000000070000000000001,10000000000000700000000000001
%N A225813 a(n) = (10^n)^2 + 7*(10^n) + 1.
%C A225813 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...x...1 when n <> 0.
%H A225813 Colin Barker, <a href="/A225813/b225813.txt">Table of n, a(n) for n = 0..499</a>
%H A225813 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A225813 From _Colin Barker_, Apr 27 2015: (Start)
%F A225813 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3).
%F A225813 G.f.: -9*(190*x^2-92*x+1)/((x-1)*(10*x-1)*(100*x-1)). (End)
%F A225813 E.g.f.: exp(x)*(1 + 7*exp(9*x) + exp(99*x)). - _Elmo R. Oliveira_, Jul 04 2025
%p A225813 A225813:=n->(10^n)^2 + 7*(10^n) + 1: seq(A225813(n), n=0..20); # _Wesley Ivan Hurt_, Apr 08 2017
%t A225813 Table[(10^n)^2 + 7*(10^n) + 1, {n, 0, 20}] (* _T. D. Noe_, Aug 12 2013 *)
%t A225813 LinearRecurrence[{111,-1110,1000},{9,171,10701},20] (* _Harvey P. Dale_, Apr 12 2020 *)
%o A225813 (PARI) Vec(-9*(190*x^2-92*x+1)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100)) \\ _Colin Barker_, Apr 27 2015
%Y A225813 Cf. A033934, A066138, A171375, A171410, A171461, A171513, A171553.
%K A225813 nonn,easy
%O A225813 0,1
%A A225813 _Lance J. Weingartz_, Jul 29 2013