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Search: id:A151252
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| A151252 |
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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, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 4, 18, 86, 414, 2026, 9962, 49220, 243940, 1211298, 6024982, 29999388, 149506288, 745566590, 3719918958, 18567624442, 92707299566, 463001495966, 2312799451962, 11554864879348, 57736384218564, 288523669037810, 1441956737106318, 7207007159715178, 36023360349838674, 180067567697351678
(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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, 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: A055834 A079567 A030278 this_sequence A084847 A082685 A111966
Adjacent sequences: A151249 A151250 A151251 this_sequence A151253 A151254 A151255
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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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