A074002 Number of elements of GF(3^n) with trace 0 and subtrace 2.

0, 0, 6, 6, 30, 72, 252, 756, 2106, 6642, 19602, 59292, 176904, 530712, 1596510, 4780782, 14351094, 43040160, 129146724, 387440172, 1162202418

Offset: 1

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Keywords

• nonn
• more

Links

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

Crossrefs

Cf. A074000, A074001, A074003, A074004, A074005.

Programs

Sage

def a(n):
    ans = 0
    for x in GF(3^n):
        if x.charpoly().coefficients(sparse=False)[-3:-1]==[2, 0]: ans += 1
    return ans  # Robin Visser, Dec 28 2024

Formula

A074000(n) + A074001(n) + a(n) = 3^(n-1) = A000244(n-1). - R. J. Mathar, Jun 14 2019

Extensions

Formula and terms a(14)-a(15) 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, 43053282, 129146724, 387440172. - Andrey Zabolotskiy, Nov 08 2024

Terms a(17)-a(20) recomputed and added again (verified that the terms a(17), a(19), a(20) conjectured by Andrey Zabolotskiy are correct), and added term a(21). - Robin Visser, Dec 28 2024