A148722 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, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 7, 25, 69, 259, 795, 3045, 9953, 38591, 131327, 513337, 1796525, 7061147, 25224451, 99529133, 361139385, 1429001559, 5248750951, 20813004833, 77196021317, 306604539891, 1146280618987, 4558515171669, 17155116612369, 68290387243567, 258421125448143, 1029533424084361, 3914217924549853

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A287880 A337016 A148721 * A148723 A148724 A332508

Adjacent sequences: A148719 A148720 A148721 * A148723 A148724 A148725

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved