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Search: id:A150084
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| A150084 |
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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, 1), (0, 0, -1), (0, 1, 0), (1, 1, 0)} |
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+0
1
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| 1, 2, 6, 19, 65, 233, 865, 3301, 12875, 51117, 205976, 840429, 3466108, 14428533, 60553582, 255966778, 1088958246, 4659451357, 20040555293, 86601741731, 375841271002, 1637517304050, 7160331688467, 31414117679299, 138246342300698, 610132138587868, 2699915527292424, 11977212862937455
(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[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A069728 A150083 A047016 this_sequence A150085 A005654 A150086
Adjacent sequences: A150081 A150082 A150083 this_sequence A150085 A150086 A150087
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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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