A074011 Number of elements of GF(5^n) with trace 1 and subtrace 2.

0, 2, 1, 30, 125, 600, 3150, 15625, 78000, 390625, 1952500, 9768750, 48815625, 244156250

Offset

1,2

Comments

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

Links

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

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

Formula

(Sage)

def a(n):

ans = 0

for x in GF(5^n):

if x.charpoly().coefficients(sparse=False)[-3:-1]==[2, 1]: ans += 1

return ans # Robin Visser, Apr 26 2024

Example

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

Crossrefs

Cf. A074006, A074007, A074008, A074009, A074010, A074012, A074013.

Sequence in context: A321442 A005693 A158419 * A054235 A016547 A081541

Adjacent sequences: A074008 A074009 A074010 * A074012 A074013 A074014

Keyword

nonn,more

Author

Frank Ruskey and Nate Kube, Aug 19 2002

Extensions

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

Status

approved