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Search: id:A150277
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| A150277 |
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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, 0), (0, 1, -1), (0, 1, 0), (1, 0, 1)} |
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+0
1
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| 1, 2, 6, 23, 89, 353, 1471, 6242, 26712, 116074, 510008, 2254425, 10033860, 44944615, 202217909, 913563797, 4143671773, 18855556442, 86046484485, 393738362852, 1806026193866, 8301731429786, 38236965932111, 176438461832407, 815503547632070, 3775140300273871, 17501159489385700, 81241736134010383
(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[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A110068 A150275 A150276 this_sequence A150278 A150279 A150280
Adjacent sequences: A150274 A150275 A150276 this_sequence A150278 A150279 A150280
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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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