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Search: id:A149212
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| A149212 |
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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, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 10, 40, 138, 569, 2207, 9475, 38862, 171853, 731033, 3296604, 14403076, 65845587, 293512383, 1355814054, 6136514157, 28582369960, 130907882612, 613896177053, 2838425700786, 13386014505024, 62374534078528, 295548379214727, 1386106527249600, 6594151582316189, 31095579594247858
(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, 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: A032121 A149210 A149211 this_sequence A007173 A114918 A149213
Adjacent sequences: A149209 A149210 A149211 this_sequence A149213 A149214 A149215
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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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