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Search: id:A149993
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| A149993 |
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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, -1, 0), (-1, 1, -1), (0, 1, 0), (1, 0, 1)} |
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+0
1
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| 1, 2, 5, 17, 59, 204, 755, 2886, 10983, 42642, 169339, 673729, 2696817, 10941944, 44610497, 182309217, 750649555, 3106888066, 12882897639, 53637560223, 224296097237, 939822049608, 3947315869157, 16633079275264, 70233934528157, 297056448537970, 1259315399665313, 5348993388208203
(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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A119254 A056679 A084528 this_sequence A148413 A149994 A149995
Adjacent sequences: A149990 A149991 A149992 this_sequence A149994 A149995 A149996
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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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