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%I #23 Sep 08 2022 08:44:44
%S 1,19,250,2830,29611,295729,2866900,27241660,255258421,2367929839,
%T 21805655950,199711092490,1821621686431,16564149750349,
%U 150264234543400,1360686332771320,12304334591153641,111146114623005259
%N Expansion of 1/((1-3x)(1-7x)(1-9x)).
%H Vincenzo Librandi, <a href="/A017998/b017998.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,-111,189).
%F a(0)=1, a(1)=19, a(2)=250, a(n)=19*a(n-1)-111*a(n-2)+189*a(n-3). - _Harvey P. Dale_, Oct 31 2011
%F a(n) = (2*9^(n+2) - 3*7^(n+2) + 3^(n+2))/24. - _Yahia Kahloune_, Jun 30 2013
%F a(n) = 16*a(n-1) -63*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013
%p a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [19, -111, 189][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 02 2013
%t CoefficientList[Series[1/((1-3x)(1-7x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[{19,-111,189},{1,19,250},30] (* _Harvey P. Dale_, Oct 31 2011 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-7*x)*(1-9*x)))); /* or */ I:=[1, 19, 250]; [n le 3 select I[n] else 19*Self(n-1)-111*Self(n-2)+189*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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