%I #10 Apr 26 2024 12:23:21

%S 1,1,1,25,125,625,3025,15625,78625,388125,1955625,9765625,48815625,

%T 244140625

%N Number of elements of GF(5^n) with trace 0 and subtrace 0.

%H F. Ruskey, <a href="http://combos.org/TSGF5">Number of Elements of GF(5^n) with given trace and subtrace</a>

%o (Sage)

%o def a(n):

%o if n==1: return 1

%o ans = 0

%o for x in GF(5^n):

%o if x.charpoly().coefficients(sparse=False)[-3:-1]==[0,0]: ans += 1

%o return ans # _Robin Visser_, Apr 26 2024

%Y Cf. A074007, A074008, A074009, A074010, A074011, A074012, A074013.

%K easy,nonn,more

%O 1,4

%A _Frank Ruskey_ and Nate Kube, Aug 19 2002

%E a(8)-a(14) from _Robin Visser_, Apr 26 2024