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A151264
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (1, -1), (1, 0)}
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0
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1, 1, 3, 6, 22, 55, 215, 607, 2465, 7506, 31246, 100251, 424703, 1416068, 6078196, 20874918, 90520934, 318287333, 1391560139, 4987827222, 21954239238, 79959969732, 353939620788, 1306665513502, 5811727596350, 21706525827949, 96945570701577, 365763459361249, 1639473277875233, 6240606814996433
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..29.
M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A148627 A148628 A148629 * A148630 A148631 A148632
Adjacent sequences: A151261 A151262 A151263 * A151265 A151266 A151267
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers, Nov 18 2008
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STATUS
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approved
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