irreducible multivariate polynomials

[Max]

Max wrote:
> Could anybody confirm my computations?
> 
> The number of irreducible monic polynomials (w.r.t. deglex order on 
> monomials) in GF(2)[x,y] of degree n=1..10:
> 6, 35, 694, 26089, 1862994, 253247715, 66799608630, 34698378752226, 
> 35781375988234520, 73534241823793715433
> 
> The number of irreducible monic polynomials in GF(3)[x,y] of degree n=1..8:
> 24, 51, 25336, 6502689, 5057781972, 11309077194436, 74762487919522380, 
> 1475282863838531153664

This one was wrong. It should be
12, 273, 25520, 6778629, 5132148528, 11368775698280, 74897449398451680, 1476178370884382958936

> The number of irreducible monic polynomials in GF(2)[x,y,z] of degree 
> n=1..6:
> 14, 903, 1034350, 34343703541, 72057077817486762, 
> 19342812032942216095260047

I have submitted these sequences along with many others related to irreducible multivariate polynomials.
Hopefully they will appear in OEIS soon under the names A115457 .. A115505.

Max