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Search: id:A087290
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| A087290 |
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Number of pairs of polynomials (f,g) in GF(3)[x] satisfying deg(f) <=n, deg(g) <= n and gcd(f,g) = 1. |
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4
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| 8, 56, 488, 4376, 39368, 354296, 3188648, 28697816, 258280328, 2324522936, 20920706408, 188286357656, 1694577218888, 15251194969976, 137260754729768, 1235346792567896
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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An unpublished result due to Stephen Suen, David desJardin, and W. Edwin Clark.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)*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
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FORMULA
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a(n) = 2*3^(2*n+1) + 2
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EXAMPLE
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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.
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CROSSREFS
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Cf. A087289, A087291, A087292.
Sequence in context: A027081 A093134 A001398 this_sequence A086787 A098914 A009107
Adjacent sequences: A087287 A087288 A087289 this_sequence A087291 A087292 A087293
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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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