A148345 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, 0), (-1, 1, -1), (0, 1, 1), (1, -1, 0)}

1, 1, 2, 5, 15, 39, 127, 405, 1330, 4478, 15574, 54337, 194625, 700396, 2559981, 9426329, 35084696, 131480551, 496179720, 1884859504, 7203732487, 27668398667, 106846816154, 414250796495, 1613369878006, 6307760507487, 24749075122327, 97443934965134, 384830938765071, 1524409052733699, 6055634647599138

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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148342 A148343 A148344 * A148346 A148347 A309299

Adjacent sequences: A148342 A148343 A148344 * A148346 A148347 A148348

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved