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Search: id:A149973
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| A149973 |
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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), (-1, 1, 1), (0, 1, 0), (1, 0, -1), (1, 0, 0)} |
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+0
1
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| 1, 2, 5, 16, 56, 204, 780, 3099, 12594, 52123, 219696, 939511, 4061334, 17733255, 78151761, 347048149, 1551225434, 6976462330, 31550130733, 143365879422, 654323444492, 2998603009552, 13792688901614, 63654344411450, 294688265919191, 1368229743361834, 6369561861745394, 29725712375089444
(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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A057973 A102461 A052708 this_sequence A149974 A149975 A149976
Adjacent sequences: A149970 A149971 A149972 this_sequence A149974 A149975 A149976
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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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