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%I #29 Dec 30 2024 16:55:42
%S 1,1,3,9,21,99,225,729,2187,6561,19845,58563,177633,531441,1594323,
%T 4782969,14344533,43059843,129127041,387420489,1162261467
%N Number of elements of GF(3^n) with trace 0 and subtrace 0.
%H Frank Ruskey, <a href="http://combos.org/TSGF3">Number of Elements of GF(3^n) with given trace and subtrace</a>
%F Appears to satisfy a linear recurrence of order 5 with signature (0, 3, 9, 18, 27). This also applies to sequences A074001-A074005. - _Andrey Zabolotskiy_, Dec 30 2024
%o (Sage)
%o def a(n):
%o if n==1: return 1
%o ans = 0
%o for x in GF(3^n):
%o if x.charpoly().coefficients(sparse=False)[-3:-1]==[0, 0]: ans += 1
%o return ans # _Robin Visser_, Dec 28 2024
%Y Cf. A074001, A074002, A074003, A074004, A074005.
%Y Cf. A073947, A053548.
%K nonn,more
%O 1,3
%A _Frank Ruskey_ and Nate Kube, Aug 19 2002
%E a(18) corrected and a(21) added by _Robin Visser_, Dec 28 2024