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Search: id:A148914
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| A148914 |
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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), (-1, 1, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1)} |
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+0
1
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| 1, 1, 3, 8, 32, 110, 440, 1668, 7012, 28078, 120543, 499524, 2184674, 9269697, 41042966, 177243697, 792410206, 3468322344, 15624044856, 69115751198, 313277217605, 1397785601261, 6368128088350, 28615558926272, 130931288440610, 591857641335827, 2718060110085283, 12348965375805603, 56892991034178925
(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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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, 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: A148911 A148912 A148913 this_sequence A148915 A151541 A022563
Adjacent sequences: A148911 A148912 A148913 this_sequence A148915 A148916 A148917
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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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