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Expansion of 1/((1-3x)(1-11x)(1-12x)).
1

%I #17 Oct 31 2023 19:09:46

%S 1,26,475,7520,110341,1545446,20980975,278565740,3637529881,

%T 46892529266,598374287875,7572794935160,95188878040621,

%U 1189735265087486,14798979200433175,183331466632763780

%N Expansion of 1/((1-3x)(1-11x)(1-12x)).

%H Vincenzo Librandi, <a href="/A018208/b018208.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 (26,-201,396).

%F G.f.: 1/((1-3*x)*(1-11*x)*(1-12*x)).

%F a(0)=1, a(1)=26, a(2)=475; for n>2, a(n) = 26*a(n-1) -201*a(n-2)+396*a(n-3). - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = 23*a(n-1) -132*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = (8*12^(n+2) - 9*11^(n+2) + 3^(n+2))/72. - _Yahia Kahloune_, Jul 07 2013

%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)

%t LinearRecurrence[{26,-201,396},{1,26,475},20] (* _Harvey P. Dale_, Jul 04 2017 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-11*x)*(1-12*x)))); /* or */ I:=[1, 26, 475]; [n le 3 select I[n] else 26*Self(n-1)-201*Self(n-2)+396*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.