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A148288
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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, 1, -1), (1, 0, 1)}
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0
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1, 1, 2, 5, 13, 33, 101, 302, 874, 2830, 9106, 28087, 93942, 313951, 1009303, 3444843, 11779708, 38944643, 134917573, 468365563, 1579283326, 5534789319, 19424123847, 66442780503, 234990336296, 831643128190, 2875768468601, 10244706374441, 36502210862689, 127302299040154, 456142329007652, 1634285147135400
(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, j, -1 + k, -1 + n] + aux[i, -1 + 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
| Sequence in context: A080888 A052988 A001429 * A112841 A104589 A154101
Adjacent sequences: A148285 A148286 A148287 * A148289 A148290 A148291
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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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