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

1,3

Comments

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

Links

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

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

Prog

(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

Crossrefs

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

Sequence in context: A154147 A179545 A163129 * A344266 A078844 A374626

Adjacent sequences: A074000 A074001 A074002 * A074004 A074005 A074006

Keyword

nonn,more

Author

Frank Ruskey and Nate Kube, Aug 19 2002

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

Status

approved