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Search: id:A148872
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| A148872 |
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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, 1), (1, -1, -1), (1, 1, -1)} |
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+0
1
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| 1, 1, 3, 8, 29, 95, 371, 1391, 5579, 22515, 93172, 389984, 1660907, 7129259, 30986277, 135626950, 598601472, 2659537838, 11888774528, 53438424419, 241407630975, 1095407211522, 4991553340467, 22831078844323, 104797432694290, 482588831392966, 2228958459777283, 10323814710499352, 47940936376648040
(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[-1 + 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, 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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Adjacent sequences: A148869 A148870 A148871 this_sequence A148873 A148874 A148875
Sequence in context: A148869 A148870 A148871 this_sequence A148873 A148874 A022017
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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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