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Search: id:A148903
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| A148903 |
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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, 1), (-1, 0, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 3, 8, 32, 101, 417, 1473, 6355, 23885, 104937, 411589, 1836969, 7422031, 33475041, 138309499, 629036675, 2644169269, 12104444055, 51586010082, 237407217744, 1023169675566, 4729538714868, 20573894111580, 95454351607666, 418509678131013, 1947864101618615, 8597770562922403, 40126065061606563
(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, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A148902 A108492 A003470 this_sequence A148904 A148905 A148906
Adjacent sequences: A148900 A148901 A148902 this_sequence A148904 A148905 A148906
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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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