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Search: id:A149840
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| A149840 |
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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), (-1, 1, -1), (0, 1, 0), (1, 0, 0)} |
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+0
1
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| 1, 2, 4, 12, 36, 105, 359, 1234, 4179, 15184, 55991, 204578, 771394, 2964054, 11327531, 43884270, 172977384, 680790080, 2693644347, 10800095655, 43381674853, 174545003823, 708672027933, 2888280123869, 11778061217176, 48301653756423, 198967324198300, 820165234102410, 3391901879073496
(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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A149837 A149838 A149839 this_sequence A025579 A010552 A149841
Adjacent sequences: A149837 A149838 A149839 this_sequence A149841 A149842 A149843
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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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