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Search: id:A149618
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| A149618 |
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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, 0, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 15, 65, 231, 1077, 4077, 19521, 77847, 375523, 1542669, 7503275, 31482945, 153831367, 656080547, 3217363353, 13890626113, 68303798347, 297856509483, 1467615828795, 6451956824907, 31844333302963, 140944569490221, 696579282949195, 3100862322964479, 15342444196387139, 68634610543557457
(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, -1 + k, -1 + n] + aux[-1 + i, 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: A149616 A066886 A149617 this_sequence A149619 A149620 A149621
Adjacent sequences: A149615 A149616 A149617 this_sequence A149619 A149620 A149621
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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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