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A148587
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, 0, 1), (0, 0, 1), (0, 1, -1), (1, 0, -1)}.
0
1, 1, 3, 6, 20, 54, 197, 606, 2327, 7790, 31007, 109983, 449032, 1661627, 6916014, 26432615, 111689208, 437872815, 1872854711, 7494986572, 32380670287, 131800276738, 574239393129, 2370817824876, 10403919136964, 43476364103039, 191976353694999, 810631010434670, 3598904531548287
OFFSET
0,3
LINKS
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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[i, j, -1 + k, -1 + n] + aux[1 + i, 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}]
CROSSREFS
Sequence in context: A148584 A148585 A148586 * A186409 A148588 A148589
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved