A148021 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, -1), (0, 0, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 2, 3, 8, 17, 46, 127, 385, 1138, 3557, 11332, 36949, 122262, 415624, 1427497, 4962532, 17550068, 62626410, 225373569, 821372128, 3016299522, 11145989333, 41593856129, 156190755015, 589476598936, 2241899251552, 8571688434648, 32908712661363, 127130928921437, 493347655801103, 1921175991853967

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148018 A148019 A148020 * A148022 A148023 A148024

Adjacent sequences: A148018 A148019 A148020 * A148022 A148023 A148024

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved