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A115489 Number of monic irreducible polynomials of degree 3 in GF(2^n)[x].

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