A192509 Number of conjugacy classes of primitive elements in GF(7^n) which have trace 0.

0, 0, 3, 20, 160, 846, 5426, 27360, 196740, 1215548, 8552408, 37330020

Offset

1,3

Comments

Also number of primitive polynomials of degree n over GF(7) whose second-highest coefficient is 0.

Links

Table of n, a(n) for n=1..12.

Formula

a(n) = A192214(n) / n.

Prog

(GAP)
p := 7;
a := function(n)
    local q, k, cnt, x;
    q:=p^n;  k:=GF(p, n);  cnt:=0;
    for x in k do
        if Trace(k, GF(p), x)=0*Z(p) and Order(x)=q-1 then
            cnt := cnt+1;
        fi;
    od;
    return cnt/n;
end;
for n in [1..16] do  Print (a(n), ", ");  od;
(Sage) # See A192507 (change first line p=3 to p=7)

Crossrefs

Cf. A152049 (GF(2^n)), A192507 (GF(3^n)), A192508 (GF(5^n)), A192510 (GF(11^n)), A192511 (GF(13^n)).

Sequence in context: A123355 A371815 A258791 * A336653 A012882 A063017

Adjacent sequences: A192506 A192507 A192508 * A192510 A192511 A192512

Keyword

nonn,hard,more

Author

Joerg Arndt, Jul 03 2011

Extensions

a(7)-a(9) from Joerg Arndt, Oct 14 2012

a(10)-a(12) from Robin Visser, Jun 01 2024

Status

approved