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Expansion of 2*x*(1-6*x+12*x^2)/(1-8*x+19*x^2-12*x^3).
1

%I #28 Dec 26 2022 09:46:53

%S 0,2,4,18,92,442,2004,8738,37132,155082,640004,2619058,10653372,

%T 43144922,174174004,701478978,2820264812,11324105962,45425564004,

%U 182089676498,729520967452,2921570654202,11696742970004,46818352939618

%N Expansion of 2*x*(1-6*x+12*x^2)/(1-8*x+19*x^2-12*x^3).

%H G. C. Greubel, <a href="/A120664/b120664.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12).

%F From _Colin Barker_, Aug 02 2012: (Start)

%F a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) for n > 3.

%F G.f.: 2*x*(1-6*x+12*x^2)/(1-8*x+19*x^2-12*x^3). (End)

%t LinearRecurrence[{8,-19,12}, {0,2,4,18}, 31] (* _G. C. Greubel_, Dec 26 2022 *)

%o (Magma) I:=[2,4,18]; [0] cat [n le 3 select I[n] else 8*Self(n-1) -19*Self(n-2) +12*Self(n-3): n in [1..31]]; // _G. C. Greubel_, Dec 26 2022

%o (SageMath)

%o @CachedFunction

%o def a(n): # a = A120664

%o if (n<4): return (0,2,4,18)[n]

%o else: return 8*a(n-1) -19*a(n-2) +12*a(n-3)

%o [a(n) for n in range(41)] # _G. C. Greubel_, Dec 26 2022

%K nonn,easy,less

%O 0,2

%A _Roger L. Bagula_, Aug 11 2006

%E Edited by _N. J. A. Sloane_, Jul 13 2007

%E New name from _Colin Barker_, Aug 02 2012