A148053 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), (1, 0, 0)}.

1, 1, 2, 3, 10, 20, 68, 147, 502, 1140, 4144, 9922, 36386, 89466, 328014, 821631, 3085210, 7905952, 29799808, 77378450, 291573466, 764676082, 2917759330, 7750067028, 29633931858, 79340993790, 303289413308, 817097085372, 3147742901542, 8549940110218, 32980631719052, 90060584656107, 347313308917902

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[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: A148050 A148051 A148052 * A148054 A148055 A089791

Adjacent sequences: A148050 A148051 A148052 * A148054 A148055 A148056

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved