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Search: id:A087292
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| A087292 |
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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. |
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+0
4
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| 0, 24, 384, 4056, 38400, 351384, 3179904, 28671576, 258201600, 2324286744, 20919997824, 188284231896, 1694570841600, 15251175838104, 137260697334144, 1235346620381016
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OFFSET
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0,2
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COMMENT
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Unpublished result due to Stephen Suen, David desJardin, and W. Edwin Clark. This 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
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FORMULA
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a(n) = 6*(3^n-1)^2
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EXAMPLE
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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.
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CROSSREFS
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Cf. A087289, A087290, A087291.
Sequence in context: A022565 A025974 A059157 this_sequence A081138 A114631 A020782
Adjacent sequences: A087289 A087290 A087291 this_sequence A087293 A087294 A087295
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KEYWORD
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easy,nonn
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AUTHOR
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W. Edwin Clark (eclark(AT)math.usf.edu), Aug 29 2003
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