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Search: id:A149162
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| A149162 |
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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, 0), (1, -1, 1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 9, 40, 115, 531, 1707, 8052, 27731, 132499, 477673, 2302126, 8577767, 41595124, 158897465, 774062896, 3015427933, 14741580123, 58341229353, 286014447954, 1146780800713, 5634802519830, 22841726382467, 112445000837320, 460097279439935, 2268513209796467, 9357465570461563, 46198374453679774
(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, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149159 A149160 A149161 this_sequence A149163 A149164 A073414
Adjacent sequences: A149159 A149160 A149161 this_sequence A149163 A149164 A149165
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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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