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A148159
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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, 0, 1), (1, -1, 1), (1, 0, 0), (1, 1, -1)}
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0
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1, 1, 2, 4, 11, 30, 101, 325, 1173, 4129, 15600, 57991, 227819, 882158, 3556595, 14196649, 58341251, 237985861, 994094162, 4126639959, 17456975753, 73516604930, 314208829825, 1338355571447, 5771924502800, 24822352236154, 107856520063495, 467688123042216, 2045200218407310, 8929933841268928
(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[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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
| Sequence in context: A141268 A135527 A148158 * A102814 A193059 A034770
Adjacent sequences: A148156 A148157 A148158 * A148160 A148161 A148162
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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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