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Search: id:A150199
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| A150199 |
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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, 0, 1), (0, 1, -1), (0, 1, 1), (1, 0, 0)} |
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+0
1
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| 1, 2, 6, 21, 79, 312, 1280, 5350, 22785, 98425, 429352, 1891118, 8390213, 37452536, 168120184, 758079627, 3432228560, 15595725843, 71086288088, 324940108298, 1489096059849, 6839618978515, 31481118065166, 145174701661390, 670635828339347, 3102980584687008, 14378436504108054, 66717350960252697
(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, 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] + 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: A033321 A050203 A112806 this_sequence A150200 A150201 A150202
Adjacent sequences: A150196 A150197 A150198 this_sequence A150200 A150201 A150202
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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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