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Search: id:A148001
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| A148001 |
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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, 0, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 2, 3, 8, 15, 39, 87, 264, 643, 1945, 5027, 15659, 41832, 134380, 376573, 1225126, 3515489, 11582825, 33844093, 112853849, 337902986, 1138451728, 3459396303, 11738577057, 36082261848, 123238143492, 384308854945, 1322121044725, 4165582957791, 14400433515567, 45736831281133, 158779022210292
(list; graph; listen)
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OFFSET
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0,3
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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, 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: A151255 A147999 A148000 this_sequence A148002 A148003 A148004
Adjacent sequences: A147998 A147999 A148000 this_sequence A148002 A148003 A148004
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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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