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Search: id:A057790
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| A057790 |
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Triangle read by rows: T(n,k) = number of knight's walks (n >= 0, k >= 0). |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 3, 4, 4, 3, 1, 1, 1, 1, 5, 5, 6, 5, 5, 1, 1, 1, 1, 6, 7, 10, 10, 7, 6, 1, 1, 1, 1, 8, 11, 16, 14, 16, 11, 8, 1, 1, 1, 1, 12, 17, 22, 27, 27, 22, 17, 12, 1, 1, 1, 1, 18, 23, 39, 44, 44, 44, 39, 23, 18, 1, 1, 1, 1
(list; table; graph; listen)
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OFFSET
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0,13
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REFERENCES
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M. Bousquet-Melou and M. Petkovsek, Linear recurrences with constant coefficients: the multivariate case, Discrete Math., 225 (2000), 51-75.
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LINKS
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M. Bousquet-M\'{e}lou, Linear recurrences with constant coefficients: the multivariate case
M. Bousquet-M\'elou and M. Petkovsek, Walks confined in a quadrant are not always D-finite
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EXAMPLE
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1; 1,1; 1,1,1; 1,1,1,1; 1,1,2,1,1; ...
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MAPLE
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T:=proc(n, k) if n=0 or n=1 or k=0 or k=1 then 1 else T(n+1, k-2)+T(n-2, k+1) fi end: seq(seq(T(n, s-n), n=0..s), s=0..15);
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CROSSREFS
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Sequence in context: A155050 A140356 A119963 this_sequence A052307 A067059 A049704
Adjacent sequences: A057787 A057788 A057789 this_sequence A057791 A057792 A057793
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 05 2000
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 23 2004
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