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Search: id:A150661
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| A150661 |
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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, 0, 1), (0, 1, 1), (1, -1, 1), (1, 0, 0), (1, 1, -1)} |
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+0
1
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| 1, 2, 7, 28, 122, 555, 2588, 12277, 58913, 285117, 1388522, 6794467, 33370370, 164371665, 811518081, 4014028257, 19884948419, 98631030741, 489728806588, 2433756380645, 12103713123846, 60232647664468, 299900743554687, 1493904068893024, 7444581364893104, 37111414613600947, 185056883908261473
(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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A010683 A150659 A150660 this_sequence A005435 A143927 A060379
Adjacent sequences: A150658 A150659 A150660 this_sequence A150662 A150663 A150664
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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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