A150467 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), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 25, 98, 394, 1627, 6860, 29349, 126916, 554542, 2441671, 10821253, 48242580, 216133921, 972469535, 4392665982, 19909498340, 90514195277, 412656103177, 1886035509909, 8639801473299, 39662054299905, 182425279994149, 840558556157834, 3879455984619635, 17932467022510137, 83009868499660146

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, -1 + j, -1 + k, -1 + n] + aux[i, 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: A150464 A150465 A150466 * A150468 A150469 A150470

Adjacent sequences: A150464 A150465 A150466 * A150468 A150469 A150470

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved