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Search: id:A150757
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| A150757 |
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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, 1, 1), (1, 0, -1), (1, 0, 1), (1, 1, 0)} |
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+0
1
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| 1, 2, 8, 29, 132, 558, 2640, 11875, 57223, 265840, 1294971, 6133682, 30085606, 144312174, 711154466, 3441237378, 17013314950, 82851670157, 410577191021, 2008989349008, 9973036413246, 48978069657381, 243459351386625, 1199080904886102, 5966497845762630, 29453453615540568, 146676039864165129
(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, k, -1 + n] + aux[-1 + i, j, -1 + 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, 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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Adjacent sequences: A150754 A150755 A150756 this_sequence A150758 A150759 A150760
Sequence in context: A150754 A150755 A150756 this_sequence A150758 A009419 A000162
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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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