A148176 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, 0, 1), (-1, 1, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 12, 28, 86, 238, 774, 2305, 7777, 24868, 85478, 286633, 1004647, 3487183, 12416017, 44263145, 159973682, 581589707, 2131952784, 7868316102, 29213757901, 109116932442, 409785142527, 1545943082568, 5863919090903, 22316371285123, 85376347850224, 327482705722678, 1262091415093097, 4875741167821283

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A381123 A151258 A148175 * A148177 A080876 A148178

Adjacent sequences: A148173 A148174 A148175 * A148177 A148178 A148179

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved