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A074010
Number of elements of GF(5^n) with trace 1 and subtrace 1.
7
0, 2, 6, 25, 125, 650, 3150, 15500, 78625, 390625, 1952500, 9768750, 48831250, 244140625
OFFSET
1,2
COMMENTS
Same as the number of elements of GF(5^n) with trace 2 and subtrace 4. Same as the number of elements of GF(5^n) with trace 3 and subtrace 4. Same as the number of elements of GF(5^n) with trace 4 and subtrace 1.
EXAMPLE
a(2;2,4)=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 2 and subtrace 4 are { 4+b, 3+4b }.
PROG
(Sage)
def a(n):
ans = 0
for x in GF(5^n):
if x.charpoly().coefficients(sparse=False)[-3:-1]==[1, 1]: ans += 1
return ans # Robin Visser, Apr 26 2024
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