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Search: id:A151088
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| A151088 |
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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), (0, 0, 1), (0, 1, -1), (1, 0, 0), (1, 0, 1)} |
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+0
1
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| 1, 3, 11, 42, 172, 731, 3190, 14185, 64088, 293148, 1353721, 6301445, 29532269, 139193588, 659208293, 3135042374, 14964198986, 71655310992, 344084815185, 1656435921209, 7992078959506, 38638407637592, 187140937165574, 907895549056257, 4411184925380861, 21461987349753724, 104551592003011526
(list; graph; listen)
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OFFSET
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0,2
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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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A117641 A084782 A149068 this_sequence A149069 A151089 A149070
Adjacent sequences: A151085 A151086 A151087 this_sequence A151089 A151090 A151091
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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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