A074001 Number of elements of GF(3^n) with trace 0 and subtrace 1.

0, 2, 0, 12, 30, 72, 252, 702, 2268, 6480, 19602, 59292, 176904, 532170, 1592136, 4785156, 14351094, 43040160, 129146724, 387400806, 1162320516

Offset: 1

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Keywords

• nonn
• more

Examples

			a(2;0,1)=2. Let GF(3^2) be defined by the field extension GF(3)[x]/( 2+b+b^2 ). The two elements of GF(3^2) with trace 0 and subtrace 1 are { 2+b, 1+2b }.
		

Links

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

Crossrefs

Cf. A074000, A074002, A074003, A074004, A074005.

Programs

Sage

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

Extensions

Terms a(13), a(15), 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, 43053282, 129146724, 387400806. - Andrey Zabolotskiy, Nov 11 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