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Search: id:A151249
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| A151249 |
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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), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 4, 17, 79, 373, 1786, 8659, 42198, 206719, 1016502, 5010965, 24758995, 122540583, 607322252, 3013490509, 14966679229, 74392292633, 370020504632, 1841498676151, 9169232578289, 45675202850061, 227608904182556, 1134592314244899, 5657369741336544, 28216228211986689, 140760455510515840
(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, -1 + j, 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: A123952 A005494 A053486 this_sequence A110307 A089165 A056096
Adjacent sequences: A151246 A151247 A151248 this_sequence A151250 A151251 A151252
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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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