A074013 Number of elements of GF(5^n) with trace 1 and subtrace 4.

0, 1, 6, 20, 125, 650, 3025, 15750, 78000, 390625, 1952500, 9765625, 48831250, 244125000

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..14.

Frank Ruskey, Number of Elements of GF(5^n) with given trace and subtrace

Example

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

Prog

(Sage)
def a(n):
    ans = 0
    for x in GF(5^n):
        if x.charpoly().coefficients(sparse=False)[-3:-1]==[4, 1]: ans += 1
    return ans  # Robin Visser, Apr 26 2024

Crossrefs

Cf. A074006, A074007, A074008, A074009, A074010, A074011, A074012.

Sequence in context: A223045 A245855 A074012 * A333896 A114959 A000386

Adjacent sequences: A074010 A074011 A074012 * A074014 A074015 A074016

Keyword

nonn,more,changed

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Extensions

a(8)-a(14) from Robin Visser, Apr 26 2024

Status

approved