A148673 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), (0, 0, -1), (1, 0, 1)}

1, 1, 3, 7, 21, 62, 201, 633, 2067, 6768, 22871, 77198, 264384, 906396, 3145281, 10935879, 38320745, 134570558, 475469721, 1683213060, 5986055526, 21332299530, 76302127859, 273399809978, 982457173368, 3536666364440, 12763021685504, 46129366899456, 167062177027460, 605905478203148, 2201414194403001

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, -1 + k, -1 + n] + aux[i, j, 1 + 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: A148670 A148671 A148672 * A141495 A151412 A121797

Adjacent sequences: A148670 A148671 A148672 * A148674 A148675 A148676

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved