A148420 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, 0, 0), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 18, 56, 190, 682, 2597, 9758, 37827, 150497, 606474, 2458196, 10128201, 42193871, 176803654, 746541792, 3180626863, 13624001336, 58635439526, 253891846471, 1104874221194, 4825290603593, 21159885596976, 93179419084287, 411616285630902, 1823604734021538, 8105569361496192

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[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A378583 A148418 A148419 * A148421 A148422 A148423

Adjacent sequences: A148417 A148418 A148419 * A148421 A148422 A148423

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved