A192212 Number of zero trace primitive elements in Galois field GF(3^n).

0, 0, 3, 8, 35, 84, 364, 832, 2997, 8700, 28281, 55080, 265720, 794304, 2006730, 5240928, 21511647, 47028492, 193587884, 415388400, 1607804226

Offset: 1

Author

Pasha Zusmanovich, Jun 25 2011

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A192211, A192213, A192214, A192215, A192216 for other primes

Programs

Sage

def a(n):
    ans = 0
    for x in GF(3^n):
        if x!=0 and x.trace()==0 and x.multiplicative_order()==3^n-1: ans += 1
    return ans  # Robin Visser, Apr 26 2024

Formula

a(n) = n * A192507(n). [Joerg Arndt, Oct 03 2012]

Extensions

a(12)-a(17) from Joerg Arndt, Oct 03 2012

a(18)-a(21) from Robin Visser, Apr 26 2024