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%I #25 May 18 2021 11:53:36
%S 11,191,1991,19991,199991,1999991,19999991,199999991,1999999991,
%T 19999999991,199999999991,1999999999991,19999999999991,
%U 199999999999991,1999999999999991,19999999999999991,199999999999999991,1999999999999999991,19999999999999999991
%N a(n) = n 9's sandwiched between two 1's.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F a(n) = 20*10^n - 9. - _Charles R Greathouse IV_, Jan 20 2012
%F a(0)=11, a(n) = 10*a(n-1) + 81.
%F From _G. C. Greubel_, Jun 22 2017: (Start)
%F G.f.: (11 + 70*x)/( (1-x)*(1-10*x) ).
%F E.g.f.: 20*exp(10*x) - 9*exp(x). (End)
%t H[n_]:=10^n+1+Sum[10^i*9,{i,1,n-1}];Array[H,100]
%t CoefficientList[Series[(11 + 70*x)/( (1-x)*(1-10*x) ), {x,0,50}], x] (* _G. C. Greubel_, Jun 23 2017 *)
%t Table[10FromDigits[PadRight[{1},n,9]]+1,{n,20}] (* or *) LinearRecurrence[ {11,-10},{11,191},20] (* _Harvey P. Dale_, May 18 2021 *)
%o (PARI) a(n)=20*10^n-9 \\ _Charles R Greathouse IV_, Jan 20 2012
%Y Cf.A132583
%K nonn,easy,less,base
%O 0,1
%A _José María Grau Ribas_, Jan 20 2012
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