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Expansion of 1/((1-3x)(1-4x)(1-10x)).
1

%I #19 Sep 08 2022 08:44:41

%S 1,17,207,2245,23231,235677,2370967,23768645,237928911,2380278637,

%T 23806803527,238084281045,2380908324991,23809346902397,

%U 238094528416887,2380949536089445,23809512411623471,238095192448290957

%N Expansion of 1/((1-3x)(1-4x)(1-10x)).

%H Vincenzo Librandi, <a href="/A016981/b016981.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 (17,-82,120).

%F a(0)=1, a(1)=17, a(2)=207, a(n)=17*a(n-1)-82*a(n-2)+120*a(n-3). - _Harvey P. Dale_, Aug 25 2012

%F a(n) = 9*3^n/7 -8*4^n/3 +50*10^n/21. - _R. J. Mathar_, Jun 23 2013

%F a(n) = 14*a(n-1) -40*a(n-2) +3^n for n>1, a(0)=1, a(1)=17. - _Vincenzo Librandi_, Jun 26 2013

%t CoefficientList[Series[1/((1-3x)(1-4x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{17,-82,120},{1,17,207},30] (* _Harvey P. Dale_, Aug 25 2012 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-4*x)*(1-10*x)))); // _Vincenzo Librandi_, Jun 26 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.