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Search: id:A149664
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| A149664 |
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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, 0), (0, -1, 1), (0, 0, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 17, 61, 249, 1003, 4115, 17371, 73519, 315575, 1367431, 5946949, 26092679, 115017031, 508924409, 2263672565, 10098869293, 45205624797, 203017643007, 913862154449, 4124692123161, 18658670407501, 84569931164973, 384100732416711, 1747491307163059, 7963465982266133, 36348101856151661
(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, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A007483 A149662 A149663 this_sequence A149665 A149666 A146444
Adjacent sequences: A149661 A149662 A149663 this_sequence A149665 A149666 A149667
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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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