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Search: id:A148943
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| A148943 |
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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, 0, 1), (0, -1, 1), (1, 1, -1), (1, 1, 0)} |
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+0
1
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| 1, 1, 3, 9, 29, 103, 367, 1337, 5023, 18933, 72019, 277595, 1072317, 4161419, 16257277, 63604357, 249494725, 982307399, 3871371275, 15281854703, 60457884995, 239348796175, 948543450125, 3764377613819, 14946670066195, 59387715592641, 236183780014071, 939637420512623, 3740066423029775
(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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A112532 A148942 A109432 this_sequence A148944 A060719 A091152
Adjacent sequences: A148940 A148941 A148942 this_sequence A148944 A148945 A148946
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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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