A148218 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), (-1, 1, -1), (1, -1, 0), (1, 0, 1)}.

1, 1, 2, 4, 13, 31, 94, 268, 906, 2645, 9319, 28964, 104652, 334941, 1249903, 4101216, 15514955, 52110795, 199934175, 683264305, 2650004523, 9184094586, 35965634307, 126280106377, 498198750670, 1766874308945, 7024092214399, 25148356140200, 100521787398542, 362740627372656, 1458173508051770

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[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A148215 A148216 A148217 * A148219 A148220 A148221

Adjacent sequences: A148215 A148216 A148217 * A148219 A148220 A148221

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved