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A148087
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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, 1), (1, 0, 0), (1, 1, -1)}
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0
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1, 1, 2, 4, 10, 23, 67, 176, 542, 1543, 4877, 14356, 47083, 143445, 480083, 1507064, 5092272, 16235880, 55737752, 180527103, 626181805, 2059548580, 7179842453, 23828111246, 83800665215, 280652471697, 993179081013, 3357496019781, 11918701536097, 40528744480241, 144678133648536, 494906147902751
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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, j, k, -1 + n] + aux[1 + i, j, -1 + 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
| Sequence in context: A205999 A124480 A130967 * A156806 A192523 A065832
Adjacent sequences: A148084 A148085 A148086 * A148088 A148089 A148090
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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