

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.


3



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

0,2


COMMENTS

Unpublished result due to Stephen Suen, David desJardins and W. Edwin Clark. This the case k = 2, q = 2 of their formula (q^(n+1)q)^k*(11/(q^(k1))) for the number of ordered ktuples (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.


LINKS

Table of n, a(n) for n=0..20.


FORMULA

a(n) = 2*(2^n1)^2.
G.f.: 2*x*(1+2*x)/((1x)*(12*x)*(14*x)).  Colin Barker, Feb 22 2012


EXAMPLE

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.


CROSSREFS

Cf. A087289, A087290, A087292.
Sequence in context: A052638 A127553 A055357 * A267691 A219758 A005969
Adjacent sequences: A087288 A087289 A087290 * A087292 A087293 A087294


KEYWORD

easy,nonn


AUTHOR

W. Edwin Clark, Aug 29 2003


STATUS

approved



