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Search: id:A149305
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| A149305 |
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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, -1, 0), (-1, 0, 1), (-1, 1, 1), (1, 0, -1), (1, 0, 1)} |
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+0
1
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| 1, 1, 4, 11, 48, 157, 707, 2547, 11728, 44793, 209515, 830425, 3928512, 15975975, 76204982, 315911451, 1516208552, 6380856199, 30770097293, 131072626339, 634440420834, 2729589294471, 13252591412098, 57494028166843, 279850008278954, 1222697025739077, 5964136075927073, 26217164510751277
(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[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149303 A053882 A149304 this_sequence A149306 A149307 A149308
Adjacent sequences: A149302 A149303 A149304 this_sequence A149306 A149307 A149308
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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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