login
Number of elements of GF(7^n) with trace 1 and subtrace 3.
9

%I #18 May 13 2024 02:13:08

%S 0,2,6,49,350,2352,16807,117992,823200,5767202,40339201,282492056

%N Number of elements of GF(7^n) with trace 1 and subtrace 3.

%C Same as the number of elements of GF(7^n) with trace 2 and subtrace 5. Same as the number of elements of GF(7^n) with trace 3 and subtrace 6. Same as the number of elements of GF(7^n) with trace 4 and subtrace 6. Same as the number of elements of GF(7^n) with trace 5 and subtrace 5. Same as the number of elements of GF(7^n) with trace 6 and subtrace 3.

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

%o (Sage)

%o def a(n):

%o ans = 0

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

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

%o return ans # _Robin Visser_, May 13 2024

%Y Cf. A074014, A074015, A074016, A074017, A074018, A074019, A074021, 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