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Search: id:A137687
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| 0, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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It is easy to show that A081399(n) is between n/log(n) and 2n/log(n) (for n>n0), cf. [Campbell 1984]. This sequence A137687 is roughly the middle of this interval (with log(n) replaced by log(n+2) to be well-defined for all n>=0), which turns out to be a fair (and simple, increasing) approximation for A081399.
See A137686 for the (signed) difference of the two sequences.
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REFERENCES
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Douglas M. Campbell, The Computation of Catalan Numbers, Mathematics Magazine, Vol. 57, No. 4. (Sep., 1984), pp. 195-208.
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LINKS
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M. F. Hasler, Table of n, a(n) for n=0,...,3000.
Douglas M. Campbell, The Computation of Catalan Numbers [JSTOR]
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PROGRAM
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(PARI) A137687(n) = round(3*n/log(n+2)/2) \\ - M. F. Hasler, Feb 06 2008
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CROSSREFS
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Cf. A000108, A001222, A081399, A120626, A137686.
Adjacent sequences: A137684 A137685 A137686 this_sequence A137688 A137689 A137690
Sequence in context: A062575 A073188 A047740 this_sequence A024745 A030581 A113609
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KEYWORD
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easy,nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 06 2008
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