A149131 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, 0, -1), (-1, 1, 1), (0, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 34, 105, 401, 1395, 5404, 20017, 78229, 301603, 1191104, 4713713, 18827432, 75824261, 306120964, 1247435845, 5085742029, 20895502425, 85932971948, 355308406475, 1472147021540, 6119409169655, 25512253280010, 106553621329117, 446477014462941, 1872849515937847, 7879862348674770

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, 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, 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: A149128 A149129 A149130 * A149132 A149133 A149134

Adjacent sequences: A149128 A149129 A149130 * A149132 A149133 A149134

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved