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Search: id:A149616
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| A149616 |
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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, -1), (-1, 0, 1), (0, 1, -1), (1, -1, 0), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 15, 63, 253, 1061, 4595, 19987, 88995, 399063, 1807047, 8258631, 37926009, 175439373, 814974117, 3803353317, 17823043081, 83783555447, 395225398493, 1869271585387, 8864339691615, 42136247375397, 200705250673001, 957981989595313, 4580559906177577, 21939160549112903, 105245130597863853
(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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A149613 A149614 A149615 this_sequence A066886 A149617 A149618
Adjacent sequences: A149613 A149614 A149615 this_sequence A149617 A149618 A149619
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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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