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%I #20 Sep 08 2022 08:44:45
%S 1,26,457,6782,91693,1170218,14373409,171896534,2016642805,
%T 23325176930,266916367081,3029497622606,34167408893437,
%U 383440973924762,4286324362209073,47766301010614598,530982729463501189
%N Expansion of 1/((1-6x)(1-9x)(1-11x)).
%H Vincenzo Librandi, <a href="/A020606/b020606.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 (26,-219,594).
%F a(0)=1, a(1)=26, a(2)=457, a(n)=26*a(n-1)-219*a(n-2)+594*a(n-3). [_Harvey P. Dale_, Oct 26 2011]
%F a(n) = (3*11^(n+2) - 5*9^(n+2) + 2*6^(n+2))/30. [_Yahia Kahloune_, Jun 30 2013]
%F a(n) = 20*a(n-1) -99*a(n-2) +6^n. - _Vincenzo Librandi_, Jul 04 2013
%t CoefficientList[Series[1 / ((1 - 6 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{26, -219, 594}, {1, 26, 457}, 20] (* _Harvey P. Dale_, Oct 26 2011 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-9*x)*(1-11*x)))); /* or */ I:=[1, 26, 457]; [n le 3 select I[n] else 26*Self(n-1)-219*Self(n-2)+594*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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