A148817 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, 0), (0, 0, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 26, 89, 317, 1145, 4349, 16621, 65495, 260108, 1050890, 4281295, 17645035, 73260909, 306735774, 1292685198, 5481962505, 23378481403, 100196337941, 431455650979, 1865578740720, 8098783460584, 35282359297779, 154228754828605, 676247512748650, 2973761506579073, 13112269586824177

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A290351 A148815 A148816 * A148818 A242903 A081497

Adjacent sequences: A148814 A148815 A148816 * A148818 A148819 A148820

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved