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%I #22 Oct 28 2017 09:41:44
%S 6,141,10401,1004001,100040001,10000400001,1000004000001,
%T 100000040000001,10000000400000001,1000000004000000001,
%U 100000000040000000001,10000000000400000000001,1000000000004000000000001,100000000000040000000000001,10000000000000400000000000001
%N a(n) = (10^n)^2 + 4*(10^n) + 1.
%C 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 Colin Barker, <a href="/A225810/b225810.txt">Table of n, a(n) for n = 0..499</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3). - _Colin Barker_, Apr 27 2015
%F G.f.: -3*(470*x^2-175*x+2) / ((x-1)*(10*x-1)*(100*x-1)). - _Colin Barker_, Apr 27 2015
%t Table[(10^n)^2 + 4*(10^n) + 1, {n, 0, 20}] (* _T. D. Noe_, Aug 12 2013 *)
%t LinearRecurrence[{111,-1110,1000},{6,141,10401},20] (* _Harvey P. Dale_, Oct 28 2017 *)
%o (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
%K nonn,easy
%O 0,1
%A _Lance J. Weingartz_, Jul 29 2013
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