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%I #22 Jun 02 2024 11:04:54
%S 0,0,3,20,160,846,5426,27360,196740,1215548,8552408,37330020
%N Number of conjugacy classes of primitive elements in GF(7^n) which have trace 0.
%C Also number of primitive polynomials of degree n over GF(7) whose second-highest coefficient is 0.
%F a(n) = A192214(n) / n.
%o (GAP)
%o p := 7;
%o a := function(n)
%o local q, k, cnt, x;
%o q:=p^n; k:=GF(p, n); cnt:=0;
%o for x in k do
%o if Trace(k, GF(p), x)=0*Z(p) and Order(x)=q-1 then
%o cnt := cnt+1;
%o fi;
%o od;
%o return cnt/n;
%o end;
%o for n in [1..16] do Print (a(n), ", "); od;
%o (Sage) # See A192507 (change first line p=3 to p=7)
%Y Cf. A152049 (GF(2^n)), A192507 (GF(3^n)), A192508 (GF(5^n)), A192510 (GF(11^n)), A192511 (GF(13^n)).
%K nonn,hard,more,changed
%O 1,3
%A _Joerg Arndt_, Jul 03 2011
%E a(7)-a(9) from _Joerg Arndt_, Oct 14 2012
%E a(10)-a(12) from _Robin Visser_, Jun 01 2024
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