cp's OEIS Frontend

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.

A087291 Number of pairs of polynomials (f,g) in GF(2)[x] satisfying 1 <= deg(f) <= n, 1 <= deg(g) <= n and gcd(f,g) = 1.

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%I A087291 #20 Aug 24 2024 21:45:51
%S A087291 0,2,18,98,450,1922,7938,32258,130050,522242,2093058,8380418,33538050,
%T A087291 134184962,536805378,2147352578,8589672450,34359214082,137437904898,
%U A087291 549753716738,2199019061250
%N A087291 Number of pairs of polynomials (f,g) in GF(2)[x] satisfying 1 <= deg(f) <= n, 1 <= deg(g) <= n and gcd(f,g) = 1.
%C A087291 Unpublished result due to Stephen Suen, _David desJardins_, and W. Edwin Clark. This is the case k = 2, q = 2 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 A087291 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -14, 8).
%F A087291 a(n) = 2*(2^n-1)^2.
%F A087291 G.f.: 2*x*(1+2*x)/((1-x)*(1-2*x)*(1-4*x)). - _Colin Barker_, Feb 22 2012
%e A087291 a(1) = 2 since gcd(x,x+1) = 1 and gcd(x+1,x) = 1 and no other pair (f,g) of polynomials in GF(2)[x] of degree 1 satisfy gcd(f,g) = 1.
%Y A087291 Cf. A087289, A087290, A087292.
%K A087291 easy,nonn
%O A087291 0,2
%A A087291 _W. Edwin Clark_, Aug 29 2003