A148878 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, 0), (0, 1, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 30, 95, 373, 1337, 5491, 20879, 87823, 348878, 1495592, 6116233, 26582687, 111153122, 488390316, 2076955693, 9206018343, 39681877464, 177159455338, 772030567083, 3467620937271, 15248904120655, 68844612742745, 305061781752215, 1383396232352037, 6170031420068042, 28088366503307858

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, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A067354 A344899 A148877 * A148879 A148880 A148881

Adjacent sequences: A148875 A148876 A148877 * A148879 A148880 A148881

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved