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%I #26 Feb 24 2024 01:13:39
%S 2,20,168,1360,10912,87360,699008,5592320,44739072,357913600,
%T 2863310848,22906490880,183251935232,1466015498240,11728124018688,
%U 93824992215040,750599937851392,6004799503073280,48038396025110528
%N Number of monic irreducible polynomials of degree 3 in GF(2^n)[x].
%H Vincenzo Librandi, <a href="/A115489/b115489.txt">Table of n, a(n) for n = 1..1000</a>
%H Max Alekseyev, <a href="http://translate.google.com/translate?hl=en&sl=ru&tl=en&u=http%3A%2F%2Fdxdy.ru%2Ftopic1165.html">Formula for the number of monic irreducible polynomials in a finite field</a>
%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI scripts for various problems</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-16).
%F a(0)=0, a(1)=2, a(n)=10a(n-1)-16a(n-2). - _T. D. Noe_, Nov 30 2006
%F G.f.: 2*x / ( (8*x-1)*(2*x-1) ). - _R. J. Mathar_, Jul 23 2014
%t LinearRecurrence[{10,-16},{2,20},30] (* _Harvey P. Dale_, Sep 25 2013 *)
%t CoefficientList[Series[2/((8 x - 1) (2 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 25 2014 *)
%o (Magma) [-(1/3)*2^n+(1/3)*8^n: n in [1..20]]; // _Vincenzo Librandi_, Jul 25 2014
%Y Cf. A115457-A115505.
%K nonn
%O 1,1
%A _Max Alekseyev_, Jan 16 2006
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