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Search: id:A148072
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| A148072 |
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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, 0), (0, 0, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 2, 4, 9, 21, 56, 148, 421, 1207, 3535, 10407, 31879, 97111, 304344, 958636, 3045621, 9696563, 31478459, 101764723, 334038583, 1100234409, 3639933291, 12057585459, 40418753669, 135042191401, 455549125751, 1540601216083, 5223311667307, 17725604119599, 60646085848546, 206928271796266, 710805289086933
(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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A106219 A032129 A005217 this_sequence A001430 A148073 A057513
Adjacent sequences: A148069 A148070 A148071 this_sequence A148073 A148074 A148075
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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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