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Search: id:A149821
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| A149821 |
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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), (0, 1, 0), (1, 0, 0)} |
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+0
1
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| 1, 2, 4, 10, 28, 80, 256, 858, 2846, 9720, 34636, 124014, 450954, 1671044, 6239162, 23442604, 89532806, 344179622, 1329638464, 5174472574, 20306201692, 79953489688, 316793120608, 1261181003246, 5043524738896, 20234227831382, 81604234177874, 330030909545484, 1339607117062318, 5452611443725374
(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, 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: A099216 A149819 A149820 this_sequence A149822 A034472 A094388
Adjacent sequences: A149818 A149819 A149820 this_sequence A149822 A149823 A149824
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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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