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Search: id:A150756
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| A150756 |
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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), (0, 1, -1), (0, 1, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 2, 8, 29, 130, 553, 2515, 11426, 52963, 247054, 1163937, 5509637, 26242160, 125450152, 602110982, 2898460907, 13991096562, 67694836745, 328216172868, 1594242682348, 7756512195064, 37792744560594, 184385163792860, 900662324391908, 4404220839977170, 21557927897972508, 105618333161600033
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A151302 A150754 A150755 this_sequence A150757 A150758 A009419
Adjacent sequences: A150753 A150754 A150755 this_sequence A150757 A150758 A150759
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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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