A115492 - OEIS

%I #19 Jun 13 2015 00:52:03

%S 35,1134,34748,1081080,34077680,1082126304,34493939648,1101659045760,

%T 35218731564800,1126449661607424,36037593107790848,

%U 1153062242078423040,36895739947165675520,1180627649514161823744,37779508323708391374848,1208935042986661734481920

%N Number of monic irreducible polynomials of degree 2 in GF(2^n)[x,y].

%H Vincenzo Librandi, <a href="/A115492/b115492.txt">Table of n, a(n) for n = 1..670</a>

%H 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 Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI scripts for various problems</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (54,-808,3456,-4096).

%F a(n) = 54*a(n-1)-808*a(n-2)+3456*a(n-3)-4096*a(n-4). - _Colin Barker_, Jul 25 2014

%F G.f.: 7*x*(256*x^2-108*x+5) / ((2*x-1)*(4*x-1)*(16*x-1)*(32*x-1)). - _Colin Barker_, Jul 25 2014

%t CoefficientList[Series[7 (256 x^2 - 108 x + 5)/((2 x - 1) (4 x - 1) (16 x - 1) (32 x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jul 26 2014 *)

%o (PARI) Vec(7*x*(256*x^2-108*x+5)/((2*x-1)*(4*x-1)*(16*x-1)*(32*x-1)) + O(x^100)) \\ _Colin Barker_, Jul 25 2014

%Y Cf. A115457-A115505.

%K nonn,easy

%O 1,1

%A _Max Alekseyev_, Jan 16 2006

%E More terms from _Colin Barker_, Jul 25 2014