A148022 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, 0), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 3, 8, 17, 48, 112, 347, 911, 2885, 7886, 26162, 76110, 255274, 759672, 2620889, 8108113, 28152858, 88374823, 312756148, 1008227273, 3582900787, 11668371798, 42040174135, 139593853572, 504390828353, 1687460696573, 6161171277397, 20919952263418, 76541691561718, 261399509898279, 964264021616684

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A148019 A148020 A148021 * A148023 A148024 A148025

Adjacent sequences: A148019 A148020 A148021 * A148023 A148024 A148025

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved