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Search: id:A149761
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| A149761 |
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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, 0), (-1, 0, 1), (0, -1, 1), (0, 0, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 19, 71, 289, 1223, 5203, 22415, 97869, 431155, 1911777, 8534569, 38305925, 172641851, 781231793, 3548304153, 16165900741, 73854023197, 338260967667, 1552835791277, 7143364707329, 32923999090571, 152014881331641, 703007464681223, 3255996384526583, 15101293781071973, 70130698637215877
(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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A083588 A149759 A149760 this_sequence A149762 A086386 A047155
Adjacent sequences: A149758 A149759 A149760 this_sequence A149762 A149763 A149764
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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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