A149362 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), (0, -1, 1), (1, 0, -1), (1, 0, 1), (1, 1, -1)}

1, 1, 4, 12, 44, 160, 630, 2505, 10274, 42813, 181411, 778323, 3376953, 14792252, 65335900, 290694175, 1301823805, 5863740425, 26550162371, 120780915859, 551812209781, 2530915409480, 11649789216869, 53800623112057, 249215824027266, 1157671306509836, 5391739956937891, 25172642088618386

Offset

0,3

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + 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: A005190 A149360 A149361 * A149363 A188632 A151460

Adjacent sequences: A149359 A149360 A149361 * A149363 A149364 A149365

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved