cp's OEIS Frontend

A115500 Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4].

%I A115500 #29 Jan 14 2024 13:36:34
%S A115500 30,340,4680,69904,1082400,17043520,270549120,4311810304,68853957120,
%T A115500 1100586419200,17600780175360,281543712968704,4504149450301440,
%U A115500 72061992352890880,1152956690052710400,18447025552981295104,295150156996346511360,4722384497336874434560,75558007841377277706240
%N A115500 Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4].
%H A115500 Vincenzo Librandi, <a href="/A115500/b115500.txt">Table of n, a(n) for n = 1..200</a>
%H A115500 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 A115500 Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI scripts for various problems</a>
%H A115500 Arnaud Bodin, <a href="http://arxiv.org/abs/0706.0157">Number of irreducible polynomials in several variables over finite fields</a>, arXiv:0706.0157 [math.AC], 2007.
%F A115500 a(n) = A020514(n) - 1, or a(n) = 2^n + 4^n + 8^n + 16^n. - _Chris Boyd_, Apr 26 2014
%F A115500 G.f.: x*(30-560*x+2880*x^2-4096*x^3)/((1-2*x)(1-4*x)(1-8*x)(1-16*x)). - _Vincenzo Librandi_, Apr 28 2014
%t A115500 CoefficientList[Series[(30 - 560 x + 2880 x^2 - 4096 x^3)/((1 - 2 x) (1 - 4 x) (1 - 8 x) (1 - 16 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)
%o A115500 (PARI) a(n) = numirrpol(2^n, 4, 1)[1]; \\ using numirrpol script from Max Alekseyev, _Michel Marcus_, Apr 28 2014
%Y A115500 Cf. A115457-A115505.
%K A115500 nonn
%O A115500 1,1
%A A115500 _Max Alekseyev_, Jan 16 2006