A074000 Number of elements of GF(3^n) with trace 0 and subtrace 0.

1, 1, 3, 9, 21, 99, 225, 729, 2187, 6561, 19845, 58563, 177633, 531441, 1594323, 4782969, 14344533, 43059843, 129127041, 387420489, 1162261467

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. A074001, A074002, A074003, A074004, A074005.

Cf. A073947, A053548.

Programs

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, 0]: ans += 1
    return ans  # Robin Visser, Dec 28 2024

Formula

Appears to satisfy a linear recurrence of order 5 with signature (0, 3, 9, 18, 27). This also applies to sequences A074001-A074005. - Andrey Zabolotskiy, Dec 30 2024

Extensions

a(18) corrected and a(21) added by Robin Visser, Dec 28 2024