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Search: id:A151068
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| A151068 |
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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), (0, 0, -1), (0, 1, 0), (0, 1, 1), (1, 0, 0)} |
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+0
1
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| 1, 3, 10, 39, 161, 677, 2928, 12960, 58017, 262405, 1199539, 5525169, 25596413, 119257971, 558421159, 2625162125, 12385172472, 58627444543, 278328330444, 1324693681144, 6319734719386, 30214893750138, 144737543240666, 694559665936562, 3338525853202416, 16071560266421005, 77475630137792744
(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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A050385 A123768 A005750 this_sequence A151069 A151070 A151071
Adjacent sequences: A151065 A151066 A151067 this_sequence A151069 A151070 A151071
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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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