A151188 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), (0, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 3, 12, 51, 230, 1066, 5037, 24081, 116155, 563954, 2751764, 13479127, 66228723, 326217488, 1610074095, 7959928866, 39407349421, 195323404901, 969088147662, 4812175829724, 23913181812753, 118907214072729, 591586601262756, 2944677520365854, 14663614748601109, 73047709533012838, 364012167715746902

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A151186 A151187 A340893 * A151189 A199875 A064036

Adjacent sequences: A151185 A151186 A151187 * A151189 A151190 A151191

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved