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Search: id:A148458
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| A148458 |
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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, 1), (-1, 0, 0), (0, 0, 1), (1, -1, 0), (1, 1, -1)} |
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+0
1
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| 1, 1, 2, 6, 18, 57, 197, 707, 2636, 10048, 39101, 155433, 626277, 2558928, 10573720, 44116907, 185795210, 788396954, 3369705436, 14493667156, 62695350738, 272644070203, 1191229217515, 5227721322572, 23033834013543, 101865871123459, 452051235815549, 2012436962585313, 8985661778362910
(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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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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Adjacent sequences: A148455 A148456 A148457 this_sequence A148459 A148460 A148461
Sequence in context: A104629 A000957 A125305 this_sequence A148459 A081057 A000137
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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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