This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A074005 #30 Dec 28 2024 09:44:19
%S A074005 0,2,3,6,30,81,252,702,2187,6642,19602,59049,176904,532170,1594323,
%T A074005 4780782,14351094,43046721,129146724,387400806,1162261467
%N A074005 Number of elements of GF(3^n) with trace 1 and subtrace 2.
%C A074005 Same as the number of elements of GF(3^n) with trace 2 and subtrace 2.
%H A074005 Frank Ruskey, <a href="http://combos.org/TSGF3">Number of Elements of GF(3^n) with given trace and subtrace</a>
%e A074005 a(2;1,2)=2. Let GF(3^2) be defined by the field extension GF(3)[x]/( 2+b+b^2 ). The two elements of GF(3^2) with trace 1 and subtrace 2 are { 1+b, 2b }.
%o A074005 (SageMath)
%o A074005 d = {(0, 0): [1], (0, 1): [0], (0, 2): [0], (1, 0): [1], (1, 1): [0], (1, 2): [0], (2, 0): [1], (2, 1): [0], (2, 2): [0]}
%o A074005 for n in (2..9):
%o A074005 for a in d.values(): a.append(0)
%o A074005 k.<u> = GF((3, n))
%o A074005 for x in k:
%o A074005 d[(x.trace(), x.charpoly().list()[-3])][-1] += 1
%o A074005 print(d[(1, 2)]) # _Andrey Zabolotskiy_, Nov 07 2024
%Y A074005 Cf. A074000, A074001, A074002, A074003, A074004.
%K A074005 nonn,more
%O A074005 1,2
%A A074005 _Frank Ruskey_ and Nate Kube, Aug 19 2002
%E A074005 a(9) and 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, 43046721, 129146724, 387400806. - _Andrey Zabolotskiy_, Nov 07 2024
%E A074005 Terms a(17)-a(20) recomputed and added again (verified that all the terms a(17)-a(20) conjectured by Andrey Zabolotskiy are correct), and added term a(21). - _Robin Visser_, Dec 28 2024