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A005223
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Number of Dyck paths of knight moves.
(Formerly M0369)
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1
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0, 0, 1, 0, 2, 2, 7, 10, 29, 52, 142, 294, 772, 1732, 4451, 10482, 26715, 64908, 165194, 409720, 1044629, 2627712, 6721492, 17079076, 43853111, 112273270, 289390434, 745262022, 1928015211, 4988699442, 12949776427, 33638741110, 87590340673
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| J. Labelle and Y.-N. Yeh, Dyck paths of knight moves, Discrete Applied Math., 24 (1989), 213-221.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| G.f.=1-1/A, where A=(1+2z+sqrt(1-4z+4z^2-4z^4)-sqrt(2)*sqrt(1-4z^2-2z^4+(2z+1)sqrt(1-4z+4z^2-4z^4)))/[4z^2].
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MATHEMATICA
| CoefficientList[Series[1-1/(((1+2z+Sqrt[1-4z+4z^2-4z^4])-Sqrt[2] Sqrt[ 1-4z^2-2z^4+(2z+1)Sqrt[1-4z+4z^2-4z^4]])/(4z^2)), {z, 0, 40}], z] (* From Harvey P. Dale, Oct 11 2011 *)
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CROSSREFS
| Sequence in context: A133374 A054226 A000024 * A118680 A094116 A079476
Adjacent sequences: A005220 A005221 A005222 * A005224 A005225 A005226
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 17 2003
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