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Search: id:A151217
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| A151217 |
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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, -1), (1, 0, 1), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 3, 13, 55, 261, 1191, 5823, 27455, 135735, 651283, 3235979, 15691615, 78165883, 381665709, 1903940151, 9341340523, 46638349691, 229624827839, 1147029010409, 5662304713031, 28293580890365, 139955523546383, 699478268799055, 3465563637240303, 17322748565123965, 85936423588182389
(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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A151214 A151215 A151216 this_sequence A151218 A151219 A006225
Adjacent sequences: A151214 A151215 A151216 this_sequence A151218 A151219 A151220
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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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