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Search: id:A149213
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| A149213 |
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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, 1), (-1, 1, 0), (1, -1, 0), (1, 1, -1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 10, 42, 133, 583, 2107, 9498, 37100, 170422, 700327, 3260691, 13885192, 65303709, 285469307, 1353084601, 6034100741, 28777781725, 130354698204, 624801809350, 2865740094979, 13792513955173, 63908250241073, 308648304990584, 1442220043930524, 6985728178113346, 32873047087774126
(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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A149212 A007173 A114918 this_sequence A149214 A149215 A149216
Adjacent sequences: A149210 A149211 A149212 this_sequence A149214 A149215 A149216
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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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