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Search: id:A149263
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| A149263 |
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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, 0, 1), (1, 0, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 4, 11, 40, 128, 484, 1641, 6334, 22270, 86616, 312454, 1220466, 4479292, 17560954, 65232393, 256488726, 961512650, 3788566998, 14305980766, 56457883232, 214441375622, 847362995744, 3233911640424, 12792266119044, 49015447106540, 194058705431670, 746071256677748, 2955972696302066
(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, 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: A149260 A149261 A149262 this_sequence A149264 A149265 A149266
Adjacent sequences: A149260 A149261 A149262 this_sequence A149264 A149265 A149266
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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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