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

30, 340, 4680, 69904, 1082400, 17043520, 270549120, 4311810304, 68853957120, 1100586419200, 17600780175360, 281543712968704, 4504149450301440, 72061992352890880, 1152956690052710400, 18447025552981295104, 295150156996346511360, 4722384497336874434560, 75558007841377277706240

Offset: 1

Author

Max Alekseyev, Jan 16 2006

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Max Alekseyev, Formula for the number of monic irreducible polynomials in a finite field
• Max Alekseyev, PARI scripts for various problems
• Arnaud Bodin, Number of irreducible polynomials in several variables over finite fields, arXiv:0706.0157 [math.AC], 2007.

Crossrefs

Cf. A115457-A115505.

Programs

Mathematica

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 *)

PARI

a(n) = numirrpol(2^n, 4, 1)[1]; \\ using numirrpol script from Max Alekseyev, Michel Marcus, Apr 28 2014

Formula

a(n) = A020514(n) - 1, or a(n) = 2^n + 4^n + 8^n + 16^n. - Chris Boyd, Apr 26 2014

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