A074021 - OEIS

%I #14 Sep 22 2025 16:00:40

%S 0,2,6,42,350,2450,16807,117306,823200,5767202,40356008,282458442

%N Number of elements of GF(7^n) with trace 1 and subtrace 4.

%C 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.

%H Frank Ruskey, <a href="http://combos.org/TSGF7">Number of Elements of GF(7^n) with given trace and subtrace</a>

%e 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 }.

%o (SageMath)

%o def a(n):

%o     ans = 0

%o     for x in GF(7^n):

%o         if x.charpoly().coefficients(sparse=False)[-3:-1]==[4, 1]: ans += 1

%o     return ans  # _Robin Visser_, May 13 2024

%Y Cf. A074014, A074015, A074016, A074017, A074018, A074019, A074020, A074022, A074023.

%K nonn,more

%O 1,2

%A _Frank Ruskey_ and Nate Kube, Aug 19 2002

%E a(8)-a(12) from _Robin Visser_, May 13 2024