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Search: id:A148845
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| A148845 |
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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, 1, 0), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 3, 8, 28, 85, 315, 1055, 4012, 13985, 54082, 193919, 757327, 2767218, 10875615, 40282189, 159004452, 594976144, 2355738462, 8884815803, 35256788279, 133810866365, 531868815609, 2028932703003, 8074680435556, 30932776387067, 123224123759839, 473724053938601, 1888553495309558
(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, 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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Sequence in context: A030495 A074271 A005641 this_sequence A148846 A163062 A148847
Adjacent sequences: A148842 A148843 A148844 this_sequence A148846 A148847 A148848
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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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