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Search: id:A149211
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| A149211 |
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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), (1, -1, 1), (1, 1, -1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 10, 40, 138, 565, 2176, 9188, 37402, 161792, 683613, 3011220, 13056815, 58330575, 257707423, 1164365165, 5218512437, 23796555039, 107869829968, 495677234473, 2267636212604, 10487894398833, 48345625875368, 224845633034712, 1043089987843812, 4874603254258163, 22737124220058175
(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, -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: A053792 A032121 A149210 this_sequence A149212 A007173 A114918
Adjacent sequences: A149208 A149209 A149210 this_sequence A149212 A149213 A149214
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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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