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Search: id:A148996
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| A148996 |
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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, -1, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 3, 9, 33, 119, 454, 1779, 7152, 29311, 122013, 514390, 2192976, 9435593, 40927132, 178767188, 785677788, 3471969333, 15417894851, 68766083151, 307921250078, 1383758689713, 6238746051177, 28211698413079, 127923279261484, 581519329356110, 2649655569254817, 12099042388429222, 55358244255747829
(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[i, 1 + 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: A148993 A148994 A148995 this_sequence A148997 A082841 A151038
Adjacent sequences: A148993 A148994 A148995 this_sequence A148997 A148998 A148999
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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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