OFFSET
0,2
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Unpublished result due to Stephen Suen, David desJardins, and W. Edwin Clark.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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (7, -14, 8).
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
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
KEYWORD
easy,nonn
AUTHOR
W. Edwin Clark, Aug 29 2003
STATUS
approved