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Search: id:A098273
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| A098273 |
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Array by antidiagonals: Number of planar lattice walks of length 3n+2k starting at (0,0) and ending at (k,0), remaining in the first quadrant, and using only NE,W,S steps. |
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+0
2
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| 1, 1, 2, 2, 8, 16, 5, 30, 96, 192, 14, 112, 480, 1408, 2816, 42, 420, 2240, 8320, 23296, 46592, 132, 1584, 10080, 44800, 153600, 417792, 835584, 429, 6006, 44352, 228480, 913920, 2976768, 7938048, 15876096, 1430, 22880, 192192, 1123584
(list; table; graph; listen)
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OFFSET
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0,3
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LINKS
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M. Bousquet-M\'elou, Walks in the quarter plane: Kreweras' algebraic model
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FORMULA
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T(n, k) = 4^n * (2k+1)/[(n+k+1)*(2n+2k+1)] * C(2k, k) * C(3n+2k, n).
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EXAMPLE
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1 2 16 192 2816 46592
1 8 96 1408 23296 417792
2 30 480 8320 153600 2976768
5 112 2240 44800 913920 19066880
14 420 10080 228480 5107200 114250752
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PROGRAM
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(PARI) T(n, k)=4^n*(2*k+1)/(n+k+1)/(2*n+2*k+1)*binomial(2*k, k)*binomial(3*n+2*k, n)
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CROSSREFS
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First row is A006335. First column is A000108 (Catalan numbers).
Adjacent sequences: A098270 A098271 A098272 this_sequence A098274 A098275 A098276
Sequence in context: A045677 A005633 A026585 this_sequence A052970 A109190 A016120
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KEYWORD
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nonn,tabl,walk
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AUTHOR
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Ralf Stephan, Sep 02 2004
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