A148084 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, -1, -1), (1, 0, 0)}.

1, 1, 2, 4, 9, 24, 68, 209, 645, 2110, 7049, 23776, 84050, 297599, 1072298, 3959753, 14643758, 55107010, 209726918, 802227580, 3108865505, 12121597818, 47579974069, 188383403156, 749420131640, 3000330585064, 12082350090766, 48870669671270, 198714418653910, 811557507388532, 3327859096146249

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, k, -1 + n] + aux[-1 + i, 1 + 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: A148082 A148083 A200966 * A156804 A081913 A092236

Adjacent sequences: A148081 A148082 A148083 * A148085 A148086 A148087

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved