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Search: id:A148919
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| A148919 |
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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, 1), (-1, 1, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 3, 8, 36, 115, 529, 1895, 8855, 33729, 160727, 637268, 3069226, 12527125, 60683485, 253007532, 1231455946, 5218227906, 25498514854, 109450738571, 536404268553, 2326770285360, 11429406175510, 50009101642780, 246121050775180, 1084761675664592, 5347280346046416, 23714434855529478
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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
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Sequence in context: A020099 A005635 A026649 this_sequence A087905 A020111 A111543
Adjacent sequences: A148916 A148917 A148918 this_sequence A148920 A148921 A148922
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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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