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Number of elements of GF(3^n) with trace 0 and subtrace 2.
5

%I #29 Dec 28 2024 09:44:06

%S 0,0,6,6,30,72,252,756,2106,6642,19602,59292,176904,530712,1596510,

%T 4780782,14351094,43040160,129146724,387440172,1162202418

%N Number of elements of GF(3^n) with trace 0 and subtrace 2.

%H Frank Ruskey, <a href="http://combos.org/TSGF3">Number of Elements of GF(3^n) with given trace and subtrace</a>

%F A074000(n) + A074001(n) + a(n) = 3^(n-1) = A000244(n-1). - _R. J. Mathar_, Jun 14 2019

%o (Sage)

%o def a(n):

%o ans = 0

%o for x in GF(3^n):

%o if x.charpoly().coefficients(sparse=False)[-3:-1]==[2, 0]: ans += 1

%o return ans # _Robin Visser_, Dec 28 2024

%Y Cf. A074000, A074001, A074003, A074004, A074005.

%K nonn,more

%O 1,3

%A _Frank Ruskey_ and Nate Kube, Aug 19 2002

%E Formula and terms a(14)-a(15) corrected, unverified terms a(17)-a(20) removed. Based on the original Data in A074000-A074005, a(17)-a(20) are possibly equal to 14351094, 43053282, 129146724, 387440172. - _Andrey Zabolotskiy_, Nov 08 2024

%E Terms a(17)-a(20) recomputed and added again (verified that the terms a(17), a(19), a(20) conjectured by Andrey Zabolotskiy are correct), and added term a(21). - _Robin Visser_, Dec 28 2024