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Number of elements of GF(7^n) with trace 1 and subtrace 5.
9

%I #17 May 13 2024 05:14:31

%S 0,0,13,42,350,2352,16807,117992,823200,5764801,40356008,282458442

%N Number of elements of GF(7^n) with trace 1 and subtrace 5.

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

%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]==[5, 1]: ans += 1

%o return ans # _Robin Visser_, May 13 2024

%Y Cf. A074014, A074015, A074016, A074017, A074018, A074019, A074020, A074021, A074023.

%K nonn,more

%O 1,3

%A _Frank Ruskey_ and Nate Kube, Aug 19 2002

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