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Search: id:A149123
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| A149123 |
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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, 1), (-1, 0, 0), (1, -1, 0), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 9, 34, 97, 373, 1215, 4768, 16429, 65917, 237771, 968122, 3580933, 14767182, 55993927, 232930254, 896421657, 3758595523, 14693407001, 61959876696, 244614547867, 1037022804734, 4138819773135, 17616327456336, 70804442020279, 302527380401375, 1225683396052321, 5252426395066506
(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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A096531 A149121 A149122 this_sequence A149124 A149125 A149126
Adjacent sequences: A149120 A149121 A149122 this_sequence A149124 A149125 A149126
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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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