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.

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

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Unpublished result due to Stephen Suen, David desJardins, and W. Edwin Clark.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

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Formula

a(n) = 6*(3^n-1)^2.

G.f.: -24*x*(3*x+1)/((x-1)*(3*x-1)*(9*x-1)). [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

Cf. A087289, A087290, A087291.

Sequence in context: A025974 A059157 A228406 * A081138 A269181 A266185

Adjacent sequences: A087289 A087290 A087291 * A087293 A087294 A087295

Keyword

easy,nonn

Author

W. Edwin Clark, Aug 29 2003

Status

approved