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Search: id:A087289
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| 3, 9, 33, 129, 513, 2049, 8193, 32769, 131073, 524289, 2097153, 8388609, 33554433, 134217729, 536870913, 2147483649, 8589934593, 34359738369, 137438953473, 549755813889, 2199023255553
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Number of pairs of polynomials (f,g) in GF(2)[x] satisfying deg(f) <=n, deg(g) <= n and gcd(f,g) = 1.
An unpublished result due to Stephen Suen, David desJardin and W. Edwin Clark. This the case k = 2, q = 2 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
Apparently the same as A084508 shifted left.
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FORMULA
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a(n) = 2^(2*n+1) + 1.
G.f.: (3-6x)/[(1-x)(1-4x)].
a(n) = 4*a(n-1) - 3. - Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 29 2005
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EXAMPLE
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a(0) = 3 since there are three pairs, (0,1), (1,0) and (1,1) of polynomials (f,g) in GF(2)[x] of degree at most 0 such that gcd(f,g) = 1.
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CROSSREFS
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Cf. A087290, A087291, A087292.
Equals A004171 + 1.
Sequence in context: A151040 A151041 A151042 this_sequence A084508 A151043 A151044
Adjacent sequences: A087286 A087287 A087288 this_sequence A087290 A087291 A087292
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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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