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A148519
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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, 0, -1), (1, 0, 1)}
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0
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1, 1, 3, 5, 17, 40, 127, 353, 1069, 3368, 10321, 33488, 105552, 343166, 1133979, 3705445, 12442819, 41163466, 138773655, 470967778, 1591257280, 5457961386, 18563391871, 63911562446, 220832875804, 761357285596, 2650206681562, 9175441031200, 32037769946372, 112122080401130, 391886258554741, 1378929978509139
(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, 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: A148518 A077796 A067062 * A148520 A148521 A148522
Adjacent sequences: A148516 A148517 A148518 * A148520 A148521 A148522
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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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