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Search: id:A151219
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| A151219 |
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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, 265, 1205, 5941, 27961, 138745, 665103, 3310317, 16041609, 79986407, 390348973, 1948432333, 9555608427, 47726348731, 234904326795, 1173682547443, 5792382066861, 28947965469611, 143162807683029, 715579210092605, 3544738294992175, 17719691563476451, 87893464730984225
(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: A151216 A151217 A151218 this_sequence A006225 A100588 A081952
Adjacent sequences: A151216 A151217 A151218 this_sequence A151220 A151221 A151222
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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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