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%I #15 Sep 08 2022 08:44:44
%S 1,19,247,2743,28063,273847,2596399,24174631,222479455,2032023895,
%T 18467516431,167287650439,1512085646527,13647818683063,
%U 123064923768943,1108992721390567,9989389232302879,89955248709321751
%N Expansion of 1/((1-4x)(1-6x)(1-9x)).
%H Vincenzo Librandi, <a href="/A019443/b019443.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 (19,-114,216).
%F a(n) = 8*4^n/5 -6*6^n +27*9^n/5. - _R. J. Mathar_, Jun 29 2013
%F a(0)=1, a(1)=19, a(2)=247; for n>2, a(n) = 19*a(n-1) -114*a(n-2) +216*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 15*a(n-1) -54*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 9 x)),{x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{19,-114,216},{1,19,247},30] (* _Harvey P. Dale_, Oct 04 2019 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-9*x)))); /* or */ I:=[1, 19, 247]; [n le 3 select I[n] else 19*Self(n-1)-114*Self(n-2)+216*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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