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.
%I A019682 #26 Aug 02 2025 12:00:47
%S A019682 1,23,363,4891,60515,710619,8059507,89191307,969344739,10390594555,
%T A019682 110181318611,1158295737963,12091317123523,125488476039131,
%U A019682 1296062772061875,13331230899395659,136647741897916067,1396496332294665147,14235133611505668499,144782868986965745195
%N A019682 Expansion of 1/((1-4*x)*(1-9*x)*(1-10*x)).
%H A019682 Vincenzo Librandi, <a href="/A019682/b019682.txt">Table of n, a(n) for n = 0..200</a>
%H A019682 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (23,-166,360).
%F A019682 a(n) = -9^(n+2)/5 +5*10^(n+1)/3+2*4^(n+1)/15. - _R. J. Mathar_, Mar 15 2011
%F A019682 a(0)=1, a(1)=23, a(2)=363; for n>2, a(n) = 23*a(n-1) -166*a(n-2) +360*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F A019682 a(n) = 19*a(n-1) -90*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013
%p A019682 a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [23, -166, 360][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 03 2013
%t A019682 CoefficientList[Series[1 / ((1 - 4 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%o A019682 (PARI) Vec(1/((1-4*x)*(1-9*x)*(1-10*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A019682 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-9*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 03 2013
%o A019682 (Magma) I:=[1, 23, 363]; [n le 3 select I[n] else 23*Self(n-1)-166*Self(n-2)+360*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K A019682 nonn,easy
%O A019682 0,2
%A A019682 _N. J. A. Sloane_