cp's OEIS Frontend

A074033 Number of degree-n irreducible polynomials over GF(4) with trace 1 and subtrace 0.

%I A074033 #24 Dec 17 2020 14:23:40
%S A074033 1,0,1,4,15,40,144,512,1841,6528,23808,87380,322875,1198080,4473647,
%T A074033 16777216,63164175,238605640,904200192,3435973836,13089461538,
%U A074033 49977753600,191219367936,733007751680,2814750270420,10825959997440,41699995927744,160842843834660
%N A074033 Number of degree-n irreducible polynomials over GF(4) with trace 1 and subtrace 0.
%C A074033 Let a = RootOf( x^2+x+1 ) and b = 1+a. Same as number of degree-n irreducible polynomials over GF(4) with trace a and subtrace 0. Same as number of degree-n irreducible polynomials over GF(4) with trace b and subtrace 0.
%H A074033 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 A074033 Frank Ruskey, <a href="http://combos.org/TSpoly4">Number of irreducible polynomials over GF(4) with given trace and subtrace</a>
%t A074033 q = 4;
%t A074033 v[t_] := If[t === 0, q - 1, -1];
%t A074033 ddp[a_, n_] := q^(n-2) + q^Quotient[n-2, 2] {v[a], -1, v[1-a], 0}[[Mod[n, 4, 1]]];
%t A074033 h[n_, 1, a_] := 1/n Sum[MoebiusMu[d] ddp[Mod[a+(d-1)/2, 2], n/d], {d, Select[Divisors[n], OddQ]}];
%t A074033 Table[h[n, 1, 0], {n, 30}] (* this sequence *)
%t A074033 Table[h[n, 1, 1], {n, 30}] (* A074034 *)
%t A074033 (* _Andrey Zabolotskiy_, Dec 17 2020 *)
%Y A074033 Cf. A074031, A074032, A074034, A074035.
%K A074033 nice,nonn
%O A074033 1,4
%A A074033 _Frank Ruskey_ and Nate Kube, Aug 26 2002
%E A074033 More terms from Ruskey's website added by _Joerg Arndt_, Jan 16 2011
%E A074033 Terms a(17) and beyond from _Andrey Zabolotskiy_, Dec 17 2020