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A149424
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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), (0, -1, 0), (0, 0, -1), (1, 1, 1)}
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0
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1, 1, 4, 13, 40, 136, 496, 1753, 6256, 22912, 85216, 314836, 1170688, 4396048, 16623328, 62744017, 237680992, 904962400, 3459831424, 13219219972, 50621972224, 194465172304, 749061374848, 2884682636764, 11126422372864, 43007603099296, 166555051934848, 644984620465264, 2500560314630656
(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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A171556 A094628 A034742 * A097112 A077284 A070428
Adjacent sequences: A149421 A149422 A149423 * A149425 A149426 A149427
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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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