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%I #19 Sep 29 2023 21:51:49
%S 1,18,223,2376,23485,222894,2067787,18935172,172107529,1557684810,
%T 14063797111,126801537408,1142367430933,10287141958566,92613721463395,
%U 833671786093884,7503791834428897,67537872487648962
%N Expansion of 1/((1-4x)(1-5x)(1-9x)).
%H Vincenzo Librandi, <a href="/A018911/b018911.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (18,-101,180).
%F a(n) = 16*4^n/5 - 25*5^n/4 + 81*9^n/20. - _R. J. Mathar_, Jun 29 2013
%F From _Vincenzo Librandi_, Jul 02 2013: (Start)
%F a(n) = 18*a(n-1) - 101*a(n-2) + 180*a(n-3) for n > 2; a(0)=1, a(1)=18, a(2)=223.
%F a(n) = 14*a(n-1) - 45*a(n-2) + 4^n. (End)
%t CoefficientList[Series[ 1 / ((1 - 4 x) (1 - 5 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)
%t LinearRecurrence[{18,-101,180},{1,18,223},30] (* _Harvey P. Dale_, Jun 22 2017 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-9*x)))); /* or */ I:=[1, 18, 223]; [n le 3 select I[n] else 18*Self(n-1)-101*Self(n-2)+180*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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