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Search: id:A150568
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| A150568 |
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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), (0, 1, -1), (1, 0, 0), (1, 1, 0)} |
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+0
1
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| 1, 2, 7, 26, 107, 462, 2053, 9357, 43312, 203180, 962555, 4596511, 22091572, 106733036, 517927304, 2522423944, 12322749650, 60357919187, 296304581671, 1457419770252, 7180626570463, 35430558631116, 175046219852421, 865804309015437, 4286686560241754, 21242694102354515, 105351540746353992
(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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A150566 A150567 A000151 this_sequence A102319 A006603 A080244
Adjacent sequences: A150565 A150566 A150567 this_sequence A150569 A150570 A150571
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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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