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Search: id:A148014
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| A148014 |
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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), (0, 0, -1), (1, 0, 0)} |
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+0
1
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| 1, 1, 2, 3, 8, 17, 46, 110, 307, 848, 2420, 6962, 20273, 61162, 185870, 568890, 1757412, 5477941, 17377747, 55272016, 176736009, 568644124, 1842453512, 6025347906, 19741386691, 64938905399, 214606827546, 712767674928, 2380612859574, 7963607476122, 26723258224939, 89989967039606, 304134328175480
(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, k, -1 + n] + aux[i, j, 1 + 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: A064954 A132333 A099965 this_sequence A148015 A148016 A148017
Adjacent sequences: A148011 A148012 A148013 this_sequence A148015 A148016 A148017
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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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