A148237 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, -1, 0), (-1, 1, 1), (0, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 105, 314, 1027, 3472, 11496, 38293, 131921, 468959, 1670355, 5889236, 21033673, 76703347, 282979446, 1038776219, 3810431891, 14145279820, 53158219229, 200235425965, 751569693745, 2830722547309, 10763132682063, 41173839901777, 157372239706242, 600900421694322, 2305586228526261

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[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A148235 A151522 A148236 * A148238 A278281 A148239

Adjacent sequences: A148234 A148235 A148236 * A148238 A148239 A148240

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved