A074023 Number of elements of GF(7^n) with trace 1 and subtrace 6.

0, 2, 6, 56, 301, 2450, 16807, 117992, 823200, 5762400, 40356008, 282475249

Offset

1,2

Comments

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

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(3;1,6)=6. Let GF(7^3) be defined by the field extension GF(7)[x]/( 3+b^2+b^3 ). The six elements of GF(7^3) with trace 1 and subtrace 6 are { 1+2b, 2+5b, 1+3b+b^2, 4+5b+b^2, 6+2b+6b^2, 2+4b+6b^2 }.

Prog

(Sage)
def a(n):
    ans = 0
    for x in GF(7^n):
        if x.charpoly().coefficients(sparse=False)[-3:-1]==[6, 1]: ans += 1
    return ans  # Robin Visser, May 13 2024

Crossrefs

Cf. A074014, A074015, A074016, A074017, A074018, A074019, A074020, A074021, A074022.

Sequence in context: A336899 A181509 A213026 * A354315 A000146 A318001

Adjacent sequences: A074020 A074021 A074022 * A074024 A074025 A074026

Keyword

easy,nonn,more

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Extensions

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

Status

approved