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A148044
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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, 0), (-1, 1, -1), (1, 0, 1)}
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0
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1, 1, 2, 3, 10, 20, 58, 119, 418, 960, 3058, 6996, 25166, 61594, 204930, 496191, 1809682, 4597480, 15689026, 39347480, 144815566, 377111538, 1308570866, 3361896292, 12453614038, 33008818730, 115909050138, 303076342734, 1128183183958, 3030390874566, 10736386125842, 28453800826831, 106322156254386
(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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A165550 A184261 A095919 * A148045 A148046 A148047
Adjacent sequences: A148041 A148042 A148043 * A148045 A148046 A148047
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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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