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Search: id:A148011
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| A148011 |
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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, 1, -1), (0, 0, 1), (0, 1, -1), (1, -1, -1)} |
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+0
1
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| 1, 1, 2, 3, 8, 15, 44, 101, 338, 849, 2736, 7555, 25254, 73321, 243290, 762927, 2557674, 8162769, 27492592, 92263125, 312597658, 1055555063, 3634419897, 12618793174, 43555825107, 151808509939, 534943761678, 1891289995128, 6664938234011, 23709504232076, 85097685030264, 304700197997170, 1093145659514525
(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, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148008 A148009 A148010 this_sequence A148012 A161178 A006882
Adjacent sequences: A148008 A148009 A148010 this_sequence A148012 A148013 A148014
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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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