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Search: id:A150673
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| A150673 |
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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), (0, 0, 1), (0, 1, -1), (0, 1, 1), (1, 0, -1)} |
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+0
1
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| 1, 2, 8, 25, 106, 399, 1777, 7262, 33233, 142659, 664407, 2943137, 13873625, 62821925, 298736121, 1374516417, 6579644721, 30642584393, 147440960403, 693166827934, 3349069169515, 15863910331592, 76906045994330, 366522699575917, 1781834382082970, 8534910654815569, 41590131826478774, 200057887714353531
(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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A150670 A150671 A150672 this_sequence A102942 A100504 A099416
Adjacent sequences: A150670 A150671 A150672 this_sequence A150674 A150675 A150676
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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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