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Search: id:A148783
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| A148783 |
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Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (0, -1, 1), (0, 1, -1), (1, 0, 1)} |
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+0
1
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| 1, 1, 3, 8, 24, 76, 251, 838, 2926, 10169, 36400, 130395, 474831, 1733605, 6403971, 23684098, 88447620, 330426207, 1243990000, 4685124726, 17751802480, 67287467042, 256301925243, 976546214354, 3736114526010, 14296501505222, 54897699531735, 210834772852983, 812124034397346, 3128637177989858
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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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, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A046342 A000958 A148782 this_sequence A084205 A118099 A066350
Adjacent sequences: A148780 A148781 A148782 this_sequence A148784 A148785 A148786
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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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