%I #11 Feb 25 2020 10:30:30
%S 8,161,10601,1006001,100060001,10000600001,1000006000001,
%T 100000060000001,10000000600000001,1000000006000000001,
%U 100000000060000000001,10000000000600000000001,1000000000006000000000001,100000000000060000000000001,10000000000000600000000000001,1000000000000006000000000000001
%N a(n) = 1 + 6*10^n + 100^n.
%H Colin Barker, <a href="/A171461/b171461.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F From _Colin Barker_, Feb 25 2020: (Start)
%F G.f.: (8 - 727*x + 1610*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)).
%F a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.
%F (End)
%F E.g.f.: exp(x)*(1 + 6*exp(9*x) + exp(99*x)). - _Stefano Spezia_, Feb 25 2020
%t Join[{8},Table[FromDigits[Join[{1},PadRight[{},n,0],{6},PadRight[{},n,0],{1}]],{n,0,10}]] (* _Harvey P. Dale_, May 15 2014 *)
%o (PARI) a(n) = 1 + 6*10^n + 100^n; \\ _Jinyuan Wang_, Feb 25 2020
%o (PARI) Vec((8 - 727*x + 1610*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^15)) \\ _Colin Barker_, Feb 25 2020
%K nonn,easy
%O 0,1
%A _Jason Earls_, Dec 09 2009
%E More terms from _Jinyuan Wang_, Feb 25 2020