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A151440
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 1), (0, 1), (1, -1), (1, 1)}
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0
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1, 1, 3, 8, 30, 104, 418, 1619, 6811, 27995, 121479, 518165, 2298497, 10057101, 45342297, 202127226, 922674852, 4172053826, 19231818364, 87941092870, 408591525432, 1885356748718, 8816855295648, 40987943515892, 192726338718178, 901557225420892, 4258807073126730, 20028060258669392
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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MATHEMATICA
| aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
| Sequence in context: A148886 A148887 A148888 * A162560 A096161 A161779
Adjacent sequences: A151437 A151438 A151439 * A151441 A151442 A151443
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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