%I #20 Sep 08 2022 08:44:43
%S 1,19,253,2935,31861,333919,3431773,34875415,352106821,3541203919,
%T 35532912493,356054541895,3564898452181,35675104315519,
%U 356907766700413,3570018022624375,35705822403011941,357092077219868719,3571123891724603533,35712457635563794855
%N Expansion of 1/((1-3x)(1-6x)(1-10x)).
%H Vincenzo Librandi, <a href="/A017952/b017952.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,-108,180).
%F a(n) = (3*10^(n+2) - 7*6^(n+2) + 4*3^(n+2))/84. - _Yahia Kahloune_, May 19 2013
%F a(0)=1, a(1)=19, a(2)=253; for n>2, a(n) = 19*a(n-1) -108*a(n-2) +180*a(n-3). - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = 16*a(n-1) -60*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, -108, 180][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 02 2013
%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 6 x) (1 - 10 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-6*x)*(1-10*x)))); /* or */ I:=[1, 19, 253]; [n le 3 select I[n] else 19*Self(n-1)-108*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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