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Search: id:A149795
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| A149795 |
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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, 1), (-1, 1, 1), (0, 1, -1), (1, -1, 1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 19, 85, 369, 1695, 7765, 36307, 170317, 807765, 3841717, 18383799, 88208733, 424946247, 2051518085, 9931383559, 48162942355, 234043500973, 1138948389163, 5551122811673, 27088130410373, 132345367637693, 647252376339615, 3168617573544485, 15525147860239259, 76130844445568163
(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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149792 A149793 A149794 this_sequence A149796 A005191 A147091
Adjacent sequences: A149792 A149793 A149794 this_sequence A149796 A149797 A149798
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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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