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A024115 a(n) = 10^n - n.

%I A024115 #26 Jan 01 2025 00:15:32
%S A024115 1,9,98,997,9996,99995,999994,9999993,99999992,999999991,9999999990,
%T A024115 99999999989,999999999988,9999999999987,99999999999986,
%U A024115 999999999999985,9999999999999984,99999999999999983,999999999999999982,9999999999999999981,99999999999999999980,999999999999999999979
%N A024115 a(n) = 10^n - n.
%H A024115 Vincenzo Librandi, <a href="/A024115/b024115.txt">Table of n, a(n) for n = 0..300</a>
%H A024115 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-21,10).
%F A024115 From _Vincenzo Librandi_, Jun 17 2013: (Start)
%F A024115 G.f.: (1-3*x+11*x^2)/((1-10*x)*(1-x)^2).
%F A024115 a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 2. (End)
%F A024115 E.g.f.: exp(x)*(exp(9*x) - x). - _Elmo R. Oliveira_, Sep 06 2024
%t A024115 Table[10^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 11 x^2) / ((1 - 10 x) (1 - x)^2),{x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 17 2013 *)
%t A024115 LinearRecurrence[{12,-21,10},{1,9,98},20] (* _Harvey P. Dale_, Jul 18 2020 *)
%o A024115 (Magma) [10^n-n: n in [0..20]]; // _Vincenzo Librandi_, Jun 30 2011
%o A024115 (Magma) I:=[1, 9, 98]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 17 2013
%o A024115 (PARI) a(n)=10^n-n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A024115 Cf. numbers of the form k^n-n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), A024076 (k=7), A024089 (k=8), A024102 (k=9), this sequence (k=10), A024128 (k=11), A024141 (k=12).
%K A024115 nonn,easy
%O A024115 0,2
%A A024115 _N. J. A. Sloane_