A150169 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, 1, -1)}.

1, 2, 6, 20, 76, 288, 1168, 4752, 20016, 84640, 365408, 1583296, 6952768, 30634624, 136213376, 607505408, 2727042560, 12274841088, 55516137984, 251692338176, 1145280189440, 5222495100928, 23883499204608, 109429258022912, 502553353359360, 2311805526441984, 10655098350616576, 49181477915541504

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, 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: A134957 A052889 A263901 * A083691 A150170 A150171

Adjacent sequences: A150166 A150167 A150168 * A150170 A150171 A150172

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved