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A074021
Number of elements of GF(7^n) with trace 1 and subtrace 4.
9
0, 2, 6, 42, 350, 2450, 16807, 117306, 823200, 5767202, 40356008, 282458442
OFFSET
1,2
COMMENTS
Same as the number of elements of GF(7^n) with trace 2 and subtrace 2. Same as the number of elements of GF(7^n) with trace 3 and subtrace 1. Same as the number of elements of GF(7^n) with trace 4 and subtrace 1. Same as the number of elements of GF(7^n) with trace 5 and subtrace 2. Same as the number of elements of GF(7^n) with trace 6 and subtrace 4.
EXAMPLE
a(2;5,2)=2. Let GF(7^2) be defined by the field extension GF(7)[x]/( 3+5b+b^2 ). The two elements of GF(7^2) with trace 5 and subtrace 2 are { 4+2b, 1+5b }.
PROG
(Sage)
def a(n):
ans = 0
for x in GF(7^n):
if x.charpoly().coefficients(sparse=False)[-3:-1]==[4, 1]: ans += 1
return ans # Robin Visser, May 13 2024
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