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Search: id:A005223
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| A005223 |
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Number of Dyck paths of knight moves.
(Formerly M0369)
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+0
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; listen)
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OFFSET
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0,5
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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).
J. Labelle and Y.-N. Yeh, Dyck paths of knight moves, Discrete Applied Math., 24 (1989), 213-221.
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FORMULA
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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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CROSSREFS
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Sequence in context: A133374 A054226 A000024 this_sequence A118680 A094116 A079476
Adjacent sequences: A005220 A005221 A005222 this_sequence A005224 A005225 A005226
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KEYWORD
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nonn,easy,nice
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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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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 17 2003
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