login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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Unpublished result due to Stephen Suen, David desJardins and W. Edwin Clark.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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)