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Search: id:A150221
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| A150221 |
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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, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, 0), (1, 1, -1)} |
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+0
1
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| 1, 2, 6, 21, 83, 349, 1528, 6885, 31663, 147881, 698854, 3333119, 16013223, 77383680, 375742768, 1831622869, 8957731740, 43928634211, 215923994375, 1063428003467, 5246221788939, 25918820316508, 128212232578680, 634919400291523, 3147189891410274, 15613197779383373, 77514351786069528
(list; graph; listen)
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OFFSET
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0,2
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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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A032347 A032346 A148495 this_sequence A063689 A058866 A087649
Adjacent sequences: A150218 A150219 A150220 this_sequence A150222 A150223 A150224
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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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