A148188 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, 0), (0, 1, -1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 12, 30, 95, 271, 935, 2912, 10474, 34733, 129609, 450096, 1724684, 6209005, 24312877, 90073297, 358940844, 1361395098, 5505083763, 21292341540, 87172110848, 342795746008, 1418408192815, 5657622195712, 23626752651759, 95409903753728, 401675130571845, 1639667774031989, 6952543492382428

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, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A148186 A006948 A148187 * A148189 A148190 A151434

Adjacent sequences: A148185 A148186 A148187 * A148189 A148190 A148191

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved