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A148451
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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, 0), (0, -1, 0), (0, 0, 1), (1, 1, -1)}
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0
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1, 1, 2, 6, 17, 51, 171, 589, 2049, 7409, 27508, 103052, 392031, 1517989, 5935172, 23393990, 93204843, 374588839, 1514534730, 6164304590, 25261163401, 104062614425, 430672375871, 1791323699173, 7484537175001, 31389035415355, 132129910409698, 558261805574402, 2366357769309447
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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
| Sequence in context: A071717 A181665 A186239 * A148452 A148453 A097514
Adjacent sequences: A148448 A148449 A148450 * A148452 A148453 A148454
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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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