A148491 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, 0, 0), (-1, 0, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 6, 21, 79, 308, 1230, 5122, 21917, 95429, 420388, 1874468, 8451916, 38469785, 176364014, 813412342, 3772468146, 17586034802, 82346756679, 387060294933, 1825485662648, 8636347518082, 40975310094819, 194907689107949, 929256234842093, 4439720262125077, 21253098983214205, 101922815438706386

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A363810 A150196 A366082 * A026737 A111279 A150197

Adjacent sequences: A148488 A148489 A148490 * A148492 A148493 A148494

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved