A150177 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, 0, 1), (1, 1, 0)}.

1, 2, 6, 20, 78, 288, 1220, 4840, 21364, 87936, 398228, 1682880, 7759528, 33369292, 155811592, 679381856, 3203272984, 14110245460, 67023556416, 297748804696, 1422910658272, 6363423616772, 30557750895420, 137442151034588, 662730771093360, 2994811386918788, 14489809853564064, 65748135236212348

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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + 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: A148485 A287424 A027215 * A150178 A150179 A150180

Adjacent sequences: A150174 A150175 A150176 * A150178 A150179 A150180

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved