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Search: id:A149316
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| A149316 |
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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, 1, 1), (1, -1, 1), (1, 1, -1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 11, 50, 184, 876, 3621, 17556, 76922, 376482, 1708220, 8409404, 39041608, 192940484, 910081407, 4509550244, 21515942178, 106817895330, 514014162986, 2555485893692, 12377644533456, 61603054201864, 299902792304566, 1493841562522540, 7302020406985320, 36395648984260868, 178487830419946360
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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, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A149313 A149314 A149315 this_sequence A149317 A027042 A051770
Adjacent sequences: A149313 A149314 A149315 this_sequence A149317 A149318 A149319
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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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