A148671 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, 1, -1), (1, 0, 1)}

1, 1, 3, 7, 21, 62, 201, 605, 2101, 6624, 23279, 76574, 271210, 918146, 3282137, 11238893, 40673789, 141042188, 513109423, 1799944820, 6574646252, 23298560696, 85395592241, 304350318826, 1120679472528, 4017613299798, 14831846057264, 53456773456522, 197791164281572, 716440662966534, 2655844304710287

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[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: A166358 A369528 A148670 * A148672 A148673 A141495

Adjacent sequences: A148668 A148669 A148670 * A148672 A148673 A148674

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved