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Search: id:A150589
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| A150589 |
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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, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 2, 7, 26, 113, 468, 2136, 9388, 43911, 199094, 944651, 4375918, 20954162, 98399067, 474273274, 2250151852, 10897911428, 52087759835, 253209013430, 1217386297913, 5935340598632, 28666246046178, 140094470568874, 679169711926961, 3325685814396341, 16171840655455189, 79319338566619733
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150587 A001862 A150588 this_sequence A007168 A150590 A006373
Adjacent sequences: A150586 A150587 A150588 this_sequence A150590 A150591 A150592
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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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