A074004 Number of elements of GF(3^n) with trace 1 and subtrace 1.

0, 1, 3, 12, 21, 81, 252, 729, 2187, 6480, 19845, 59049, 176904, 531441, 1594323, 4785156, 14344533, 43046721, 129146724, 387420489, 1162261467

Offset

1,3

Comments

Same as the number of elements of GF(3^n) with trace 2 and subtrace 1.

Links

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

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

Example

a(3;2,1)=3. Let GF(3^3) be defined by the field extension GF(3)[x]/( 1+b+2b^2+b^3 ). The three elements of GF(3^3) with trace 2 and subtrace 1 are { 2b, 1+b^2, 1+b+2b^2 }.

Prog

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

Crossrefs

Cf. A074000, A074001, A074002, A074003, A074005.

Sequence in context: A091846 A061262 A051656 * A088099 A375986 A110419

Adjacent sequences: A074001 A074002 A074003 * A074005 A074006 A074007

Keyword

nonn,more

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Extensions

a(14) corrected, unverified terms a(17)-a(20) removed. Based on the original Data in A074000-A074005, a(17)-a(20) are possibly equal to 14344533, 43046721, 129146724, 387420489. - 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