A074017 Number of elements of GF(7^n) with trace 1 and subtrace 0.

1, 0, 6, 42, 350, 2450, 16807, 117649, 823200, 5762400, 40356008, 282492056

Offset

1,3

Comments

Same as the number of elements of GF(7^n) with trace 2 and subtrace 0. Same as the number of elements of GF(7^n) with trace 3 and subtrace 0. Same as the number of elements of GF(7^n) with trace 4 and subtrace 0. Same as the number of elements of GF(7^n) with trace 5 and subtrace 0. Same as the number of elements of GF(7^n) with trace 6 and subtrace 0.

Links

Table of n, a(n) for n=1..12.

Frank Ruskey, Number of Elements of GF(7^n) with given trace and subtrace

Prog

(Sage)
def a(n):
    if n==1: return 1
    ans = 0
    for x in GF(7^n):
        if x.charpoly().coefficients(sparse=False)[-3:-1]==[0, 1]: ans += 1
    return ans  # Robin Visser, May 13 2024

Crossrefs

Cf. A074014, A074015, A074016, A074018, A074019, A074020, A074021, A074022, A074023.

Sequence in context: A232473 A300693 A222062 * A135887 A218817 A368321

Adjacent sequences: A074014 A074015 A074016 * A074018 A074019 A074020

Keyword

nonn,more

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Extensions

a(8)-a(12) from Robin Visser, May 13 2024

Status

approved