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A074035 Let a = RootOf( x^2+x+1 ) and b = 1+a. Number of degree-n irreducible polynomials over GF(4) with trace 1 and subtrace a.

%I A074035 #32 Dec 18 2020 04:25:14
%S A074035 0,1,1,4,12,45,144,512,1813,6579,23808,87380,322560,1198665,4473647,
%T A074035 16777216,63160320,238612920,904200192,3435973836,13089411609,
%U A074035 49977848925,191219367936,733007751680,2814749599332,10825961287995,41699995927744,160842843834660
%N A074035 Let a = RootOf( x^2+x+1 ) and b = 1+a. Number of degree-n irreducible polynomials over GF(4) with trace 1 and subtrace a.
%C A074035 Same as number of degree-n irreducible polynomials over GF(4) with trace 1 and subtrace b. Same as number of degree-n irreducible polynomials over GF(4) with trace a and subtrace 1. Same as number of degree-n irreducible polynomials over GF(4) with trace a and subtrace a. Same as number of degree-n irreducible polynomials over GF(4) with trace b and subtrace 1. Same as number of degree-n irreducible polynomials over GF(4) with trace b and subtrace b.
%H A074035 E. N. Kuz'min, <a href="https://doi.org/10.1007/BF00971203">Irreducible polynomials over a finite field and an analogue of Gauss sums over a field of characteristic 2</a>, Siberian Mathematical Journal, 32, 982-989 (1991).
%H A074035 Frank Ruskey, <a href="http://combos.org/TSpoly4">Number of irreducible polynomials over GF(4) with given trace and subtrace</a>, The Combinatorial Object Server.
%t A074035 q = 4;
%t A074035 ddpx[n_] := q^(n-2) + q^Quotient[n-2, 2] {-1, 1, -1, 0}[[Mod[n, 4, 1]]];
%t A074035 h1x[n_] :=  1/n Sum[MoebiusMu[d] ddpx[n/d], {d, Select[Divisors[n], OddQ]}];
%t A074035 Table[h1x[n], {n, 30}]
%t A074035 (* _Andrey Zabolotskiy_, Dec 17 2020 *)
%Y A074035 Cf. A074031, A074032, A074033, A074034.
%K A074035 nice,nonn
%O A074035 1,4
%A A074035 _Frank Ruskey_ and Nate Kube, Aug 26 2002
%E A074035 More terms from Ruskey's website added by _Joerg Arndt_, Jan 16 2011
%E A074035 Terms a(17) and beyond from _Andrey Zabolotskiy_, Dec 17 2020