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 A074001 #23 Dec 28 2024 09:44:23
%S A074001 0,2,0,12,30,72,252,702,2268,6480,19602,59292,176904,532170,1592136,
%T A074001 4785156,14351094,43040160,129146724,387400806,1162320516
%N A074001 Number of elements of GF(3^n) with trace 0 and subtrace 1.
%H A074001 Frank Ruskey, <a href="http://combos.org/TSGF3">Number of Elements of GF(3^n) with given trace and subtrace</a>
%e A074001 a(2;0,1)=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 0 and subtrace 1 are { 2+b, 1+2b }.
%o A074001 (Sage)
%o A074001 def a(n):
%o A074001 ans = 0
%o A074001 for x in GF(3^n):
%o A074001 if x.charpoly().coefficients(sparse=False)[-3:-1]==[1, 0]: ans += 1
%o A074001 return ans # _Robin Visser_, Dec 28 2024
%Y A074001 Cf. A074000, A074002, A074003, A074004, A074005.
%K A074001 nonn,more
%O A074001 1,2
%A A074001 _Frank Ruskey_ and Nate Kube, Aug 19 2002
%E A074001 Terms a(13), a(15), a(16) 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, 387400806. - _Andrey Zabolotskiy_, Nov 11 2024
%E A074001 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