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Search: id:A148997
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| A148997 |
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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, 0, 0), (-1, 0, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1)} |
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+0
1
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| 1, 1, 3, 9, 33, 121, 468, 1859, 7558, 31270, 131330, 558115, 2396603, 10379648, 45292679, 198926208, 878692550, 3900981744, 17396764823, 77896353911, 350065380105, 1578398595372, 7138256186788, 32371596240950, 147175354377729, 670685606484390, 3062947647863016, 14016157023522647
(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, j, -1 + k, -1 + n] + aux[1 + i, 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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Adjacent sequences: A148994 A148995 A148996 this_sequence A148998 A148999 A149000
Sequence in context: A148994 A148995 A148996 this_sequence A082841 A151038 A039648
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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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