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Search: id:A151295
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| A151295 |
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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, 0), (0, -1), (0, 1), (1, -1), (1, 0)} |
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+0
1
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| 1, 2, 7, 24, 93, 364, 1490, 6178, 26163, 112001, 485272, 2120168, 9336512, 41376649, 184414880, 825963661, 3715457866, 16777860859, 76025036272, 345560464513, 1575102460028, 7197823974471, 32968875212361, 151333039522219, 696010343742969, 3206893602486167, 14800691952029228, 68415758808948051
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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M. Bouquet-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[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, 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: A003041 A026558 A150402 this_sequence A150403 A150404 A150405
Adjacent sequences: A151292 A151293 A151294 this_sequence A151296 A151297 A151298
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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