A148128 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, 1, -1), (-1, 1, 0), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 11, 26, 75, 226, 694, 2124, 6964, 22651, 74306, 252118, 870230, 2985640, 10429931, 36910773, 130430664, 465185889, 1683090537, 6096731410, 22153416883, 81263153490, 298937740181, 1101577014304, 4090030072618, 15254096109545, 56942298278323, 213478556276168, 803556605025425, 3028267343205841

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[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A148125 A148126 A148127 * A148129 A340651 A123432

Adjacent sequences: A148125 A148126 A148127 * A148129 A148130 A148131

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved