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%I #25 Dec 11 2024 06:38:51
%S 1,18,235,2760,31141,345918,3819295,42071220,463025881,5094274218,
%T 56041033555,616467614880,6781209278221,74593565712918,
%U 820530282235015,9025837356505740,99284227972292161,1092126576027270018
%N Expansion of 1/((1-3x)(1-4x)(1-11x)).
%H Vincenzo Librandi, <a href="/A017065/b017065.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,-89,132).
%F a(n) = 9*3^n/8 - 16*4^n/7 + 121*11^n/56. - _R. J. Mathar_, Jun 23 2013
%F From _Vincenzo Librandi_, Jun 26 2013: (Start)
%F a(n) = 18*a(n-1) - 89*a(n-2) + 132*a(n-3).
%F a(n) = 15*a(n-1) - 44*a(n-2) + 3^n. (End)
%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 4 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 26 2013 *)
%t LinearRecurrence[{18,-89,132},{1,18,235},20] (* _Harvey P. Dale_, Jul 28 2023 *)
%o (Magma) I:=[1,18,235]; [n le 3 select I[n] else 18*Self(n-1)-89*Self(n-2)+132*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jun 26 2013
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-4*x)*(1-11*x)))); // _Vincenzo Librandi_, Jun 26 2013
%o (PARI) x='x+O('x^20); Vec(1/((1-3*x)*(1-4*x)*(1-11*x))) \\ _Altug Alkan_, Sep 23 2018
%K nonn,easy,changed
%O 0,2
%A _N. J. A. Sloane_