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A149143
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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, -1, 1), (-1, 0, 1), (0, -1, 1), (1, 1, 0)}
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0
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1, 1, 4, 9, 36, 115, 415, 1533, 5620, 21745, 81919, 321111, 1253400, 4935875, 19638310, 78189715, 314738408, 1265989251, 5129667839, 20842916637, 84946968208, 347484625799, 1424371713680, 5858750057523, 24138658791448, 99705765074263, 412686733202823, 1711263384187145, 7109205179311358
(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[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149140 A149141 A149142 * A149144 A149145 A001256
Adjacent sequences: A149140 A149141 A149142 * A149144 A149145 A149146
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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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