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 A087292 #21 Aug 24 2024 21:45:25 %S A087292 0,24,384,4056,38400,351384,3179904,28671576,258201600,2324286744, %T A087292 20919997824,188284231896,1694570841600,15251175838104, %U A087292 137260697334144,1235346620381016,11118120616550400,100063088648317464,900567807132948864,8105110292090814936 %N A087292 Number of pairs of polynomials (f,g) in GF(3)[x] satisfying 1 <= deg(f) < =n, 1 <= deg(g) <= n and gcd(f,g) = 1. %C A087292 Unpublished result due to Stephen Suen, _David desJardins_, and W. Edwin Clark. This is the case k = 2, q = 3 of their formula (q^(n+1)-q)^k*(1-1/(q^(k-1))) for the number of ordered k-tuples (f_1, ..., f_k) of polynomials in GF(q)[x] such that 1 <= deg(f_i) <= n for all i and gcd(f_1, ..., f_k) = 1. %H A087292 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-39,27). %F A087292 a(n) = 6*(3^n-1)^2. %F A087292 G.f.: -24*x*(3*x+1)/((x-1)*(3*x-1)*(9*x-1)). [_Colin Barker_, Sep 05 2012] %e A087292 There are 6 polynomials in GF(3)[x] of degree 1. a(1) = 24 since the 6*4 = 24 ordered pairs (f,g) where g is not equal to f or 2f are the only ordered pairs of polynomials of degree 1 satisfying gcd(f,g) = 1. %Y A087292 Cf. A087289, A087290, A087291. %K A087292 easy,nonn %O A087292 0,2 %A A087292 _W. Edwin Clark_, Aug 29 2003