A148505 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), (0, 0, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 3, 5, 17, 34, 121, 275, 1007, 2570, 9421, 26616, 95957, 294055, 1038947, 3391255, 11823571, 40442112, 140588537, 496156778, 1735133067, 6234168269, 22062124755, 79968394842, 287166124521, 1045564777399, 3809206698457, 13920813110374, 51328211536803, 188484694277612, 700930984869221, 2590430782376645

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[i, j, 1 + 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: A156761 A151261 A148504 * A148506 A148507 A148508

Adjacent sequences: A148502 A148503 A148504 * A148506 A148507 A148508

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved