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Search: id:A005566
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| A005566 |
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Number of walks of length n on square lattice, starting at origin, staying in first quadrant.
(Formerly M1627)
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+0
9
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| 1, 2, 6, 18, 60, 200, 700, 2450, 8820, 31752, 116424, 426888, 1585584, 5889312, 22084920, 82818450, 312869700, 1181952200, 4491418360, 17067389768, 65166397296, 248817153312, 953799087696, 3656229836168, 14062422446800
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Contribution from Eric Egge (eegge(AT)carleton.edu), Oct 21 2008: (Start)
a(n) is the number of involutions of length 2n which are invariant
under the reverse-complement map and have no decreasing subsequences
of length 5. (End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
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FORMULA
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a(n) = binomial(n, [n/2])*binomial(n+1, [(n+1)/2])
E.g.f.: (BesselI(0, 2*x)+BesselI(1, 2*x))^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2003
EXPCONV of A001405 with itself, i.e. a(n) = sum_{k=0}^n binomial(n,k)*A001405(k)*A001405(n-k) - Max Alekseyev (maxale(AT)gmail.com), May 18 2006
(16*x^2-1)*hypergeom([3/2, 3/2],[2],16*x^2)+(1/(2x)+2)*hypergeom([1/2, 1/2],[1],16*x^2)-1/(2x) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Oct 13 2009]
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CROSSREFS
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Cf. A001700, A060897-A060900.
a(2*n) = A000894(n), a(2*n+1) = 2*A060150(n+1).
Sequence in context: A148460 A148461 A002527 this_sequence A005631 A118677 A150043
Adjacent sequences: A005563 A005564 A005565 this_sequence A005567 A005568 A005569
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Additional comments from David W. Wilson (davidwwilson(AT)comcast.net), May 05 2001
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