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Search: id:A148295
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| A148295 |
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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), (0, 1, 0), (1, -1, 0)} |
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+0
1
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| 1, 1, 2, 5, 13, 35, 110, 348, 1125, 3843, 13148, 45611, 162558, 586159, 2131427, 7874167, 29269092, 109441041, 413029164, 1569707723, 5997195310, 23061664488, 89112018445, 345612962634, 1346404338661, 5267594366529, 20682129410605, 81495668391418, 322182388464667, 1277141667228060, 5076304190905437
(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[i, -1 + j, 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: A148292 A148293 A148294 this_sequence A046171 A022854 A116409
Adjacent sequences: A148292 A148293 A148294 this_sequence A148296 A148297 A148298
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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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