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.

0, 2, 18, 98, 450, 1922, 7938, 32258, 130050, 522242, 2093058, 8380418, 33538050, 134184962, 536805378, 2147352578, 8589672450, 34359214082, 137437904898, 549753716738, 2199019061250

Offset: 0

Author

W. Edwin Clark, Aug 29 2003

Keywords

• easy
• nonn

Comments

Unpublished result due to Stephen Suen, David desJardins, and W. Edwin Clark.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.

Examples

			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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7, -14, 8).

Crossrefs

Cf. A087289, A087290, A087292.

Formula

a(n) = 2*(2^n-1)^2.

G.f.: 2*x*(1+2*x)/((1-x)*(1-2*x)*(1-4*x)). - Colin Barker, Feb 22 2012