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Search: id:A148077
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| A148077 |
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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, 1), (0, 1, -1), (1, 0, 0)} |
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+0
1
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| 1, 1, 2, 4, 9, 24, 60, 171, 482, 1397, 4253, 12734, 39807, 124496, 393876, 1271415, 4091866, 13406172, 44050521, 145678352, 486558215, 1626299970, 5484672863, 18549475207, 63002376085, 215196629904, 736195482482, 2531826112640, 8727353541961, 30175242044617, 104712273647938, 363933649177806, 1269272249934532
(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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A080376 A005669 A038664 this_sequence A148078 A093156 A148079
Adjacent sequences: A148074 A148075 A148076 this_sequence A148078 A148079 A148080
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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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