A148194 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, 0), (-1, -1, 1), (-1, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 12, 32, 111, 339, 1270, 4228, 16660, 58812, 239932, 883852, 3698244, 14070761, 60020868, 234232378, 1014341312, 4040258419, 17709836885, 71738276020, 317595021922, 1304766472942, 5824447742137, 24216797341207, 108863181794207, 457318226423684, 2068167875135848, 8766255585444469

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, j, 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, 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: A216818 A216819 A216820 * A289501 A274961 A027695

Adjacent sequences: A148191 A148192 A148193 * A148195 A148196 A148197

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved