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Search: id:A133871
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| A133871 |
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a(n) = the definite integral int_{0..1} prod_{j=1..n} 4 sin^2(pi jx)dx. |
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+0
1
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| 2, 4, 6, 10, 12, 20, 24, 34, 44, 64, 78, 116, 148, 208, 286, 410, 556, 808, 1120, 1620, 2308, 3352, 4784, 6980, 10064, 14680, 21296
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OFFSET
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1,1
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COMMENT
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This quantity arises in some examples associated to the dynamical Mertens' theorem for quasihyperbolic toral automorphisms.
The function being integrated to compute a_n vanishes on the set of points in the Farey sequence of level n. I am particularly interested in knowing how large the sequence is asymptotically.
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REFERENCES
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Sawian Jaidee, Shaun Stevens and Thomas Ward; Mertens' theorem for toral automorphisms, preprint 2008.
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EXAMPLE
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a(2)=4 since \int_0^1 sin^2(\pi x)sin^2(2\pi x) dx = 1/4.
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MAPLE
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int(product(4*(sin(Pi*j*x))^2, j=1..9), x=0..1);
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CROSSREFS
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Cf. A005728.
Sequence in context: A064374 A000885 A068336 this_sequence A068514 A074645 A125286
Adjacent sequences: A133868 A133869 A133870 this_sequence A133872 A133873 A133874
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KEYWORD
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nonn
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AUTHOR
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Thomas Ward (t.ward(AT)uea.ac.uk), Jan 07 2008
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