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A149339
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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, 0), (-1, 0, 1), (0, -1, 0), (1, 0, -1), (1, 1, 0)}
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0
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1, 1, 4, 12, 40, 151, 573, 2233, 9134, 37319, 156741, 667054, 2860003, 12451013, 54546675, 240872936, 1072716219, 4799044185, 21612759421, 97809065210, 444495198056, 2029640845007, 9299375495917, 42763721937159, 197309308044494, 912930646489117, 4236548432117128, 19709480208088418
(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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149336 A149337 A149338 * A149340 A180889 A002996
Adjacent sequences: A149336 A149337 A149338 * A149340 A149341 A149342
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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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