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Search: id:A148503
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| A148503 |
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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, 0, 1), (0, 1, -1), (1, 0, -1)} |
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+0
1
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| 1, 1, 3, 5, 15, 37, 123, 369, 1215, 3873, 13439, 46389, 166211, 587241, 2139343, 7853281, 29436835, 110256257, 417088191, 1589755941, 6134996203, 23788716713, 92647968427, 362538770889, 1429592471767, 5669395402541, 22564924805887, 90077402253757, 361286842382159, 1456188214956373, 5890364709523459
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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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[i, -1 + j, 1 + k, -1 + n] + aux[i, 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
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Sequence in context: A146212 A018516 A138017 this_sequence A145939 A161703 A018551
Adjacent sequences: A148500 A148501 A148502 this_sequence A148504 A148505 A148506
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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