A087290 Number of pairs of polynomials (f,g) in GF(3)[x] satisfying deg(f) <= n, deg(g) <= n and gcd(f,g) = 1.

8, 56, 488, 4376, 39368, 354296, 3188648, 28697816, 258280328, 2324522936, 20920706408, 188286357656, 1694577218888, 15251194969976, 137260754729768, 1235346792567896, 11118121133111048, 100063090197999416, 900567811781994728, 8105110306037952536

Offset: 0

Author

W. Edwin Clark, Aug 29 2003

Keywords

• easy
• nonn

Comments

An unpublished result due to Stephen Suen, David desJardins, and W. Edwin Clark.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)*k) * (1 - 1/q^(k-1) + (q-1)/q^((n+1)*k)) for the number of ordered k-tuples (f_1, ..., f_k) of polynomials in GF(q)[x] such that deg(f_i) <= n for all i and gcd(f_1, ..., f_k) = 1.

Examples

			a(0) = 8 since there are eight pairs, (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), (2,2) of polynomials (f,g) in GF(3)[x] of degree at most 0 such that gcd(f,g) = 1.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-9).

Crossrefs

Cf. A087289, A087291, A087292.

Programs

Mathematica

2*3^(2Range[0,30]+1)+2 (* or *) LinearRecurrence[{10,-9},{8,56},30] (* Harvey P. Dale, Mar 07 2012 *)

Formula

a(n) = 2*3^(2*n+1) + 2.

a(n) = 10*a(n-1) - 9*a(n-2), a(0)=8, a(1)=56. - Harvey P. Dale, Mar 07 2012

G.f.: 8*(1-3*x)/((1-x)*(1-9*x)). - Colin Barker, Apr 16 2012

Extensions

More terms from Harvey P. Dale, Mar 07 2012