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A151082
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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), (0, 1, 1), (1, 0, 0), (1, 0, 1)}
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0
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1, 3, 10, 41, 173, 759, 3397, 15544, 71901, 335279, 1578727, 7477889, 35591302, 170128077, 816596947, 3930930312, 18972648915, 91803771609, 445155659067, 2162359819683, 10521285811683, 51271661812391, 250178483978304, 1222186872046030, 5977382665897160, 29263117871361351, 143389975617232829
(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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + 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
| Sequence in context: A153474 A151081 A152802 * A151083 A140046 A116540
Adjacent sequences: A151079 A151080 A151081 * A151083 A151084 A151085
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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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