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%I #16 Sep 08 2022 08:44:45
%S 1,18,233,2718,30549,338706,3736561,41145606,452775917,4981233114,
%T 54796358409,602771123214,6630527086405,72935976891042,
%U 802296461596577,8825263940808342,97077914802006813,1067857108634797290
%N Expansion of 1/((1-x)(1-2x)(1-4x)(1-11x)).
%H Vincenzo Librandi, <a href="/A021094/b021094.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 (18,-91,162,-88).
%F a(n) = -(1/30)+(4/9)*2^n-(32/21)*4^n+(1331/630)*11^n. [_Antonio Alberto Olivares_, May 22 2012]
%F a(0)=1, a(1)=18; for n>1, a(n) = 15*a(n-1) -44*a(n-2) +2^n - 1. - _Vincenzo Librandi_, Jul 06 2013
%F a(0)=1, a(1)=18, a(2)=233, a(3)=2718; for n>3, a(n) = 18*a(n-1) -91*a(n-2) +162*a(n-3) -88*a(n-4). - _Vincenzo Librandi_, Jul 06 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 06 2013 *)
%t LinearRecurrence[{18, -91, 162, -88}, {1, 18, 233, 2718}, 20] (* _Robert G. Wilson v_, Jul 06 2013 *)
%o (Magma) I:=[1, 18, 233, 2718]; [n le 4 select I[n] else 18*Self(n-1)-91*Self(n-2)+162*Self(n-3)-88*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 06 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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