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%I #14 Sep 08 2022 08:44:43
%S 1,19,258,3110,35651,399609,4433668,48962380,539552901,5939935199,
%T 65363612678,719121544050,7910946538951,87023461294789,
%U 957273325857288,10530082856852120,115831292830529801,1274146128290750379
%N Expansion of 1/((1-3x)(1-5x)(1-11x)).
%H Vincenzo Librandi, <a href="/A017917/b017917.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 (19,-103,165).
%F a(0)=1, a(1)=19, a(2)=258; for n>2, a(n) = 19*a(n-1) -103*a(n-2) +165*a(n-3). - _Vincenzo Librandi_, Jul 01 2013
%F a(n) = 16*a(n-1) -55*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 01 2013
%F a(n) = (11^(n+2) - 4*5^(n+2) + 3^(n+3))/48. [_Yahia Kahloune_, Jul 06 2013]
%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 11 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o (Magma) I:=[1, 19, 258]; [n le 3 select I[n] else 19*Self(n-1)-103*Self(n-2)+165*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-5*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 01 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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