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Search: id:A151083
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| A151083 |
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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), (-1, 1, -1), (0, 1, 1), (1, 0, 0), (1, 0, 1)} |
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+0
1
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| 1, 3, 10, 41, 173, 759, 3406, 15618, 72354, 338120, 1594023, 7562099, 36031901, 172424727, 828339131, 3990698554, 19274402605, 93318527436, 452731903409, 2200129435723, 10709121191503, 52203448696454, 254795042352594, 1245027406344003, 6090268253018489, 29820535800079680, 146141006117111445
(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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A151081 A152802 A151082 this_sequence A140046 A116540 A000248
Adjacent sequences: A151080 A151081 A151082 this_sequence A151084 A151085 A151086
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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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