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A148169
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), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.
0
1, 1, 2, 4, 11, 31, 103, 342, 1223, 4392, 16506, 62556, 244133, 960293, 3851560, 15555730, 63698508, 262461123, 1092521898, 4572692026, 19288640555, 81754788980, 348654622331, 1493144372062, 6426427761938, 27761268531353, 120419760141811, 524043699721912, 2288472222005169, 10022411092677579
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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + 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, -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: A148167 A148168 A004251 * A110140 A190452 A275426
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved