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Search: id:A150567
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| A150567 |
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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, 0, 0), (0, 0, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 2, 7, 26, 107, 457, 2016, 9065, 41424, 191529, 894019, 4204565, 19897098, 94641154, 452107980, 2167676408, 10425903303, 50282484818, 243082789531, 1177611502760, 5715528217575, 27786221354972, 135284133335976, 659545295681644, 3219346412950448, 15731435487175994, 76949340577947377
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150564 A150565 A150566 this_sequence A000151 A150568 A102319
Adjacent sequences: A150564 A150565 A150566 this_sequence A150568 A150569 A150570
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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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