A148988 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, 0), (0, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 33, 114, 439, 1689, 6816, 27624, 114988, 482122, 2052197, 8800591, 38111226, 166113251, 729043557, 3217041687, 14269984543, 63581058548, 284464187518, 1277397712864, 5755627288014, 26013095364631, 117900835435171, 535755079557245, 2440363785685090, 11140458053301700, 50961594352233542

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[-1 + i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A176812 A192430 A323790 * A148989 A047117 A148990

Adjacent sequences: A148985 A148986 A148987 * A148989 A148990 A148991

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved