

A087292


Number of pairs of polynomials (f,g) in GF(3)[x] satisfying 1 <= deg(f) < =n, 1 <= deg(g) <= n and gcd(f,g) = 1.


3



0, 24, 384, 4056, 38400, 351384, 3179904, 28671576, 258201600, 2324286744, 20919997824, 188284231896, 1694570841600, 15251175838104, 137260697334144, 1235346620381016, 11118120616550400, 100063088648317464, 900567807132948864, 8105110292090814936
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OFFSET

0,2


COMMENTS

Unpublished result due to Stephen Suen, David desJardins, and W. Edwin Clark. This is the case k = 2, q = 3 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



FORMULA

a(n) = 6*(3^n1)^2.
G.f.: 24*x*(3*x+1)/((x1)*(3*x1)*(9*x1)). [Colin Barker, Sep 05 2012]


EXAMPLE

There are 6 polynomials in GF(3)[x] of degree 1. a(1) = 24 since the 6*4 = 24 ordered pairs (f,g) where g is not equal to f or 2f are the only ordered pairs of polynomials of degree 1 satisfying gcd(f,g) = 1.


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



