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Search: id:A148040
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| A148040 |
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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), (0, 1, -1), (1, 0, -1), (1, 0, 0)} |
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+0
1
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| 1, 1, 2, 3, 8, 19, 55, 152, 475, 1462, 4746, 15587, 53395, 183704, 645336, 2304003, 8369954, 30628353, 113457813, 425476602, 1610303851, 6134996528, 23581388253, 91405898719, 356438621366, 1397836274856, 5518769111515, 21915664391127, 87424025172871, 350422697792128, 1411783576129019, 5711966700811943
(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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + 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: A078343 A148038 A148039 this_sequence A148041 A148042 A077269
Adjacent sequences: A148037 A148038 A148039 this_sequence A148041 A148042 A148043
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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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