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Search: id:A148042
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| A148042 |
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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), (0, 1, -1), (1, 0, 0), (1, 1, -1)} |
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+0
1
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| 1, 1, 2, 3, 8, 19, 57, 165, 535, 1700, 5761, 19596, 69357, 247143, 904969, 3344222, 12578803, 47771691, 183784047, 713153652, 2795057882, 11038817438, 43945343994, 176118626035, 710510882943, 2883088313211, 11764647473938, 48250711908615, 198849105981280, 823144145532963, 3421816206647552
(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, k, -1 + n] + aux[i, -1 + j, 1 + 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: A148039 A148040 A148041 this_sequence A077269 A148043 A007999
Adjacent sequences: A148039 A148040 A148041 this_sequence A148043 A148044 A148045
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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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