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Expansion of 1/((1-4x)(1-5x)(1-11x)).
2

%I #19 Sep 30 2023 09:18:12

%S 1,20,281,3460,40161,453300,5048041,55853540,616079921,6785596180,

%T 74686191801,821775473220,9040683799681,99453356876660,

%U 1094016369479561,12034328357198500,132378357688767441

%N Expansion of 1/((1-4x)(1-5x)(1-11x)).

%H Vincenzo Librandi, <a href="/A019040/b019040.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20,-119,220).

%F a(n) = 16*4^n/7 - 25*5^n/6 + 121*11^n/42. - _R. J. Mathar_, Jun 29 2013

%F From _Vincenzo Librandi_, Jul 02 2013: (Start)

%F a(n) = 20*a(n-1) - 119*a(n-2) + 220*a(n-3) for n > 2; a(0)=1, a(1)=20, a(2)=281.

%F a(n) = 16*a(n-1) - 55*a(n-2) + 4^n. (End)

%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 5 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-11*x)))); /* or */ I:=[1, 20, 281]; [n le 3 select I[n] else 20*Self(n-1)-119*Self(n-2)+220*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_