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%I A020343 #12 Sep 08 2022 08:44:45
%S A020343 1,22,327,4100,46781,503202,5201827,52278640,514595961,4986022382,
%T A020343 47721236927,452316244380,4253691236341,39747202125562,
%U A020343 369442770633627,3418759065309320,31519177212527921,289676122850156742
%N A020343 Expansion of 1/((1-5x)(1-8x)(1-9x)).
%H A020343 Vincenzo Librandi, <a href="/A020343/b020343.txt">Table of n, a(n) for n = 0..200</a>
%H A020343 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (22,-157,360).
%F A020343 a(n) = 25*5^n/12 -64*8^n/3 +81*9^n/4. - _R. J. Mathar_, Jun 29 2013
%F A020343 a(0)=1, a(1)=22, a(3)=327; for n>2, a(n) = 22*a(n-1) -157*a(n-2) +360*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F A020343 a(n) = 17*a(n-1) -72*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013
%t A020343 CoefficientList[Series[1 / ((1 - 5 x) (1 - 8 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%o A020343 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-8*x)*(1-9*x)))); /* or */ I:=[1, 22, 327]; [n le 3 select I[n] else 22*Self(n-1)-157*Self(n-2)+360*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K A020343 nonn,easy
%O A020343 0,2
%A A020343 _N. J. A. Sloane_.

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