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%I #17 Jul 02 2023 18:14:58
%S 0,2,18,98,450,1922,7938,32258,130050,522242,2093058,8380418,33538050,
%T 134184962,536805378,2147352578,8589672450,34359214082,137437904898,
%U 549753716738,2199019061250
%N 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%C Unpublished result due to Stephen Suen, _David desJardins_, and W. Edwin Clark.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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -14, 8).
%F a(n) = 2*(2^n-1)^2.
%F G.f.: 2*x*(1+2*x)/((1-x)*(1-2*x)*(1-4*x)). - _Colin Barker_, Feb 22 2012
%e 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 Cf. A087289, A087290, A087292.
%K easy,nonn
%O 0,2
%A _W. Edwin Clark_, Aug 29 2003
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