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

1,3

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

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

Prog

(SageMath)
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

Crossrefs

Cf. other traces and subtraces: A074001, A074002, A074003, A074004, A074005.

Cf. A073947, A053548.

Cf. other characteristic: A038518, A074006, A074014.

Sequence in context: A218003 A146909 A146248 * A067645 A101474 A298836

Adjacent sequences: A073997 A073998 A073999 * A074001 A074002 A074003

Keyword

nonn,more

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Extensions

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

Status

approved