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Search: id:A005222
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| A005222 |
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Number of Dyck paths of knight moves.
(Formerly M3234)
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+0
1
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| 1, 0, 1, 0, 4, 4, 18, 26, 86, 158, 462, 976, 2665, 6082, 16040, 38338, 99536, 244880, 631923, 1583796, 4081939, 10358670, 26728731, 68425494, 176964795, 455967376, 1182454137, 3061954102, 7962768190, 20702327552, 53983118006, 140817757006
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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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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FORMULA
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G.f.: A+z^4A^3/(1-zA)^2, 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: A086448 A128090 A119948 this_sequence A133039 A035413 A087213
Adjacent sequences: A005219 A005220 A005221 this_sequence A005223 A005224 A005225
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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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