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Search: id:A149554
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| A149554 |
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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, 0, 0), (-1, 1, 0), (1, -1, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 13, 59, 187, 883, 3169, 14959, 56465, 270401, 1067643, 5138107, 20768155, 100531397, 415371639, 2018477663, 8463235109, 41253849485, 175193128703, 856236442631, 3673538468941, 17990245877423, 77839901320289, 381879487570937, 1664511334644829, 8177969008270369, 35866951221369105
(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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A084136 A091147 A149553 this_sequence A149555 A149556 A149557
Adjacent sequences: A149551 A149552 A149553 this_sequence A149555 A149556 A149557
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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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