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Search: id:A003059
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| 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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n+1 first appears in the sequence at the A002522(n)-th entry (since the ultimate occurrence of n is n^2). a(n) refers to the greatest minimal length of monotone subsequence (i.e.either increasing or decreasing) contained within any sequence of n distinct numbers,according to the Erdos-Szekeres theorem - Lekraj Beedassy (blekraj(AT)yahoo.com), May 20 2003
a(n) = SUM(A010052(k): 0 <= k < n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 01 2009]
With offset 0, apparently the least k such that binomial(2n,n-k) < (1/e) binomial(2n,n). [From T. D. Noe (noe(AT)sspectra.com), Mar 12 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
M. Somos, Sequences used for indexing triangular or square arrays
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FORMULA
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a(n) = ceiling(sqrt(n)).
G.f.: (Sum_{n>=0} x^(n^2))x/(1-x). - Michael Somos, May 03, 2003
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PROGRAM
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(PARI) a(n)=if(n<1, 0, 1+sqrtint(n-1))
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CROSSREFS
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A000196, A000290, A157466. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 01 2009]
Sequence in context: A083375 A088519 A135034 this_sequence A011752 A025790 A030617
Adjacent sequences: A003056 A003057 A003058 this_sequence A003060 A003061 A003062
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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