A148819 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, 1, -1), (1, 1, 0)}.

1, 1, 3, 8, 26, 92, 311, 1161, 4418, 16770, 66734, 264292, 1066008, 4380303, 17942834, 74820454, 313808725, 1319581995, 5616581050, 23932844268, 102589135624, 442708044443, 1912059874482, 8310231577525, 36231490886389, 158281403031522, 694917637204853, 3055506420550141, 13473895432254104

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[-1 + i, -1 + 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: A081497 A028270 A124383 * A148820 A148821 A074506

Adjacent sequences: A148816 A148817 A148818 * A148820 A148821 A148822

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved