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Search: id:A149652
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| A149652 |
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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), (-1, 1, 1), (1, 0, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 15, 73, 253, 1249, 4715, 23383, 92777, 461363, 1889779, 9412703, 39414289, 196524667, 836368379, 4173239663, 17983252335, 89776734151, 390717706879, 1951269037821, 8561073114893, 42766026014581, 188901443388587, 943828751049715, 4192840338848059, 20952333831534239, 93535812613094543
(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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + 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: A149649 A149650 A149651 this_sequence A151487 A101553 A149653
Adjacent sequences: A149649 A149650 A149651 this_sequence A149653 A149654 A149655
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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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