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

1,3

Links

Table of n, a(n) for n=1..21.

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

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A279865 A377186 A321528 * A359741 A140959 A015699

Adjacent sequences: A073999 A074000 A074001 * A074003 A074004 A074005

Keyword

nonn,more

Author

Frank Ruskey and Nate Kube, Aug 19 2002

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

Status

approved