%I #16 Sep 08 2022 08:44:43

%S 1,20,283,3518,41209,468608,5247271,58277666,644406997,7108612676,

%T 78315612739,862197157094,9488521761265,104399859167624,

%U 1148555174389087,12635047273900202,138991162189670413

%N Expansion of 1/((1-3x)(1-6x)(1-11x)).

%H Vincenzo Librandi, <a href="/A017953/b017953.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 (20,-117,198).

%F a(0)=1, a(1)=20, a(2)=283; for n>2, a(n) = 20*a(n-1) -117*a(n-2) +198*a(n-3). - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = 17*a(n-1) -66*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = (3*11^(n+2) - 8*6^(n+2) + 5*3^(n+2))/120. [_Yahia Kahloune_, Jul 06 2013]

%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 6 x) (1 - 11 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)

%t LinearRecurrence[{20,-117,198},{1,20,283},30] (* _Harvey P. Dale_, Aug 31 2020 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-6*x)*(1-11*x)))); /* or */ I:=[1, 20, 283]; [n le 3 select I[n] else 20*Self(n-1)-117*Self(n-2)+198*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.