A151208 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), (0, 1, 0), (1, 0, 1), (1, 1, -1), (1, 1, 1)}

1, 3, 12, 54, 252, 1205, 5838, 28512, 140142, 691450, 3422482, 16976693, 84352809, 419663169, 2089896141, 10415635115, 51940595958, 259142066138, 1293408024950, 6457548605162, 32248465078285, 161079058749138, 804714766489242, 4020727101627926, 20091696454820064, 100408276629560143

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A151206 A151207 A083881 * A055835 A366118 A362597

Adjacent sequences: A151205 A151206 A151207 * A151209 A151210 A151211

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved