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Search: id:A150658
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| A150658 |
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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, 0, 1), (0, 1, -1), (1, -1, 1), (1, 1, 0)} |
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+0
1
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| 1, 2, 7, 28, 120, 536, 2457, 11481, 54360, 259969, 1252706, 6072223, 29572252, 144564197, 708884636, 3484931078, 17168524909, 84731554148, 418805940619, 2072716595002, 10269460176509, 50929639896861, 252786813629413, 1255605670244016, 6240630233618970, 31034662772521170, 154411925525049741
(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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A005436 A150656 A150657 this_sequence A026770 A010683 A150659
Adjacent sequences: A150655 A150656 A150657 this_sequence A150659 A150660 A150661
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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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