cp's OEIS Frontend

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.

A024116 a(n) = 10^n - n^2.

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%I A024116 #19 Jul 08 2025 17:28:06
%S A024116 1,9,96,991,9984,99975,999964,9999951,99999936,999999919,9999999900,
%T A024116 99999999879,999999999856,9999999999831,99999999999804,
%U A024116 999999999999775,9999999999999744,99999999999999711,999999999999999676
%N A024116 a(n) = 10^n - n^2.
%H A024116 Vincenzo Librandi, <a href="/A024116/b024116.txt">Table of n, a(n) for n = 0..300</a>
%H A024116 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (13,-33,31,-10).
%F A024116 G.f.: (1-4*x+12*x^2+9*x^3)/((1-10*x)*(1-x)^3). - _Vincenzo Librandi_, Oct 06 2014
%F A024116 a(n) = 13*a(n-1) -33*a(n-2) +31*a(n-3) -10*a(n-4) for n>3. - _Vincenzo Librandi_, Oct 06 2014
%F A024116 a(n) = A011557(n) - A000290(n). - _Michel Marcus_, Oct 06 2014
%t A024116 Table[10^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 12 x^2 + 9 x^3)/((1 - 10 x) (1-x)^3), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 06 2014 *)
%t A024116 LinearRecurrence[{13,-33,31,-10},{1,9,96,991},20] (* _Harvey P. Dale_, May 29 2021 *)
%o A024116 (Magma) [10^n-n^2: n in [0..20]]; // _Vincenzo Librandi_, Jun 30 2011
%Y A024116 Cf. similar sequences listed in A024025.
%K A024116 nonn,easy
%O A024116 0,2
%A A024116 _N. J. A. Sloane_