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A074031 Number of degree-n irreducible polynomials over GF(4) with trace 0 and subtrace 0.

%I A074031 #28 Dec 16 2020 05:55:06
%S A074031 1,0,2,0,15,40,153,480,1841,6528,23901,87040,322875,1198080,4474738,
%T A074031 16773120,63164175,238605640,904213989,3435921408,13089461538,
%U A074031 49977753600,191219550297,733007052640,2814750270420,10825959997440,41699998413248,160842834247680
%N A074031 Number of degree-n irreducible polynomials over GF(4) with trace 0 and subtrace 0.
%H A074031 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 A074031 Frank Ruskey, <a href="http://combos.org/TSpoly4">Number of irreducible polynomials over GF(4) with given trace and subtrace</a>
%t A074031 k = 2; q = 2^k;
%t A074031 v[t_] := If[t === 0, q - 1, -1];
%t A074031 dd[a_, n_] := With[{m = Floor[(n + 1)/4]},
%t A074031    q^(n - 2) + Switch[Mod[n, 4],
%t A074031      2, 0,
%t A074031      0, -v[a] q^((n - 2)/2) (-1)^(m k),
%t A074031      _, v[a] q^((n - 3)/2) (-1)^(m k)
%t A074031    ]];
%t A074031 h[n_, 0, a_] := 1/n Sum[MoebiusMu[d] (dd[a, n/d] - Boole[EvenQ[n]] q^(n/(2d)-1)), {d, Select[Divisors[n], OddQ]}];
%t A074031 Table[h[n, 0, 0], {n, 30}] (* this sequence *)
%t A074031 Table[h[n, 0, 1], {n, 30}] (* A074032 *)
%t A074031 (* _Andrey Zabolotskiy_, Dec 15 2020 *)
%Y A074031 Cf. A074032, A074033, A074034, A074035.
%K A074031 nice,nonn
%O A074031 1,3
%A A074031 _Frank Ruskey_ and Nate Kube, Aug 26 2002
%E A074031 More terms from Ruskey's website added by _Joerg Arndt_, Jan 16 2011
%E A074031 Terms a(17) and beyond from _Andrey Zabolotskiy_, Dec 15 2020