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Search: id:A150088
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| A150088 |
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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, 0, 1), (0, 1, 0), (1, -1, -1), (1, 1, 0)} |
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+0
1
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| 1, 2, 6, 19, 66, 243, 930, 3676, 14903, 61584, 258894, 1103447, 4758012, 20732432, 91124592, 403681327, 1800752730, 8081803201, 36474901389, 165435268106, 753751636931, 3448465225387, 15836193654948, 72977234653985, 337370456592555, 1564255503416559, 7272766119061584, 33899558103994633
(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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + 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: A005654 A150086 A150087 this_sequence A150089 A150090 A150091
Adjacent sequences: A150085 A150086 A150087 this_sequence A150089 A150090 A150091
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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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