A148236 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, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 13, 35, 125, 379, 1410, 4568, 17355, 58687, 226060, 787594, 3063243, 10908565, 42712542, 154643162, 608400479, 2231231403, 8808890240, 32636886464, 129188068662, 482614611622, 1914179241594, 7199755293220, 28600519629207, 108188009568027, 430294291549040, 1635533474861490

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, k, -1 + n] + aux[1 + i, -1 + 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: A189597 A148235 A151522 * A148237 A148238 A278281

Adjacent sequences: A148233 A148234 A148235 * A148237 A148238 A148239

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved