A074019 Number of elements of GF(7^n) with trace 1 and subtrace 2.

0, 1, 6, 56, 350, 2352, 16807, 117306, 825601, 5762400, 40356008, 282458442

Offset

1,3

Comments

Same as the number of elements of GF(7^n) with trace 2 and subtrace 1. Same as the number of elements of GF(7^n) with trace 3 and subtrace 4. Same as the number of elements of GF(7^n) with trace 4 and subtrace 4. Same as the number of elements of GF(7^n) with trace 5 and subtrace 1. Same as the number of elements of GF(7^n) with trace 6 and subtrace 2.

Links

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

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

Example

a(2;3,4)=1. Let GF(7^2) be defined by the field extension GF(7)[x]/( 3+5b+b^2 ). The one element of GF(7^2) with trace 3 and subtrace 4 is { 5 }.

Prog

(Sage)
def a(n):
    ans = 0
    for x in GF(7^n):
        if x.charpoly().coefficients(sparse=False)[-3:-1]==[2, 1]: ans += 1
    return ans  # Robin Visser, May 13 2024

Crossrefs

Cf. A074014, A074015, A074016, A074017, A074018, A074020, A074021, A074022, A074023.

Sequence in context: A364471 A097126 A210325 * A074018 A074016 A183513

Adjacent sequences: A074016 A074017 A074018 * A074020 A074021 A074022

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