Analogy of sequence A027424 for GF(2)[x]

[Yuval Dekel]

Let R be the polynomial ring GF(2)[x] and
a(n) = Number of distinct products f*g with f,g in R and  1 <= deg(f),deg(g) 
<= n .

Can someone compute a(n) ?

Thanks,
Yuval

http://www.research.att.com/projects/OEIS?Anum=A027424

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