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A150657
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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, 0, 1), (0, 0, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}
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0
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1, 2, 7, 28, 120, 533, 2434, 11333, 53506, 255229, 1227000, 5935322, 28852938, 140820142, 689529978, 3385401557, 16658845955, 82130513718, 405568719091, 2005502756025, 9928819372100, 49206031236460, 244077436803703, 1211648687439490, 6018998734519270, 29918170650355973, 148791763397361989
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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
| Sequence in context: A150655 A005436 A150656 * A150658 A026770 A010683
Adjacent sequences: A150654 A150655 A150656 * A150658 A150659 A150660
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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