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Search: id:A150043
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| A150043 |
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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, 0, 1), (0, 1, 1), (1, 1, -1)} |
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+0
1
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| 1, 2, 6, 18, 60, 204, 716, 2560, 9296, 34128, 126560, 472864, 1778016, 6722880, 25536768, 97384128, 372691968, 1430618112, 5506231808, 21244025088, 82137286400, 318177976064, 1234689470976, 4798686523904, 18676787597824, 72786442978304, 283997288733696, 1109305183011840, 4337384738945024
(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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A005566 A005631 A118677 this_sequence A048117 A048118 A004113
Adjacent sequences: A150040 A150041 A150042 this_sequence A150044 A150045 A150046
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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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