A151066 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), (0, 0, 1), (1, 0, 0), (1, 1, 0)}.

1, 3, 10, 39, 156, 656, 2843, 12506, 56183, 254799, 1167999, 5400258, 25116348, 117576380, 552896051, 2611402749, 12381025083, 58885700834, 280918838846, 1343547473970, 6440935983886, 30943137348073, 148936555890019, 718126779191896, 3468065435753711, 16772888745124827, 81229159839429236

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A149051 A151064 A151065 * A151067 A007163 A219263

Adjacent sequences: A151063 A151064 A151065 * A151067 A151068 A151069

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved