A074003 Number of elements of GF(3^n) with trace 1 and subtrace 0.

1, 0, 3, 9, 30, 81, 225, 756, 2187, 6561, 19602, 59049, 177633, 530712, 1594323, 4782969, 14351094, 43046721, 129127041, 387440172, 1162261467

Offset: 1

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Keywords

• nonn
• more

Comments

Same as the number of elements of GF(3^n) with trace 2 and subtrace 0.

Links

• Frank Ruskey, Number of Elements of GF(3^n) with given trace and subtrace

Crossrefs

Cf. A074000, A074001, A074002, A074004, A074005.

Programs

Sage

def a(n):
    if n==1: return 1
    ans = 0
    for x in GF(3^n):
        if x.charpoly().coefficients(sparse=False)[-3:-1]==[0, 1]: ans += 1
    return ans  # Robin Visser, Dec 28 2024

Extensions

Terms a(13)-a(16) corrected, unverified terms a(17)-a(20) removed. Based on the original Data in A074000-A074005, a(17)-a(20) are possibly equal to 14351094, 43046721, 129127041, 387440172. - Andrey Zabolotskiy, Nov 11 2024

Terms a(17)-a(20) recomputed and added again (verified that all the terms a(17)-a(20) conjectured by Andrey Zabolotskiy are correct), and added term a(21). - Robin Visser, Dec 28 2024