A150271 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, 1, 1), (0, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 2, 6, 22, 91, 383, 1668, 7411, 33476, 152897, 707145, 3299234, 15490659, 73143589, 347167321, 1654542464, 7912965246, 37970582001, 182724292495, 881421183634, 4261082344830, 20641085036137, 100163243902972, 486821506316846, 2369576128859998, 11549163118691787, 56357043289847950, 275312066835176586

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A308564 A226435 A292318 * A150272 A342289 A124293

Adjacent sequences: A150268 A150269 A150270 * A150272 A150273 A150274

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved