A150250 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), (0, 0, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 22, 85, 339, 1395, 5878, 25192, 109323, 479306, 2119594, 9440676, 42302795, 190529094, 861966149, 3914794199, 17840793760, 81552762664, 373801093673, 1717515358487, 7908884731531, 36491882034611, 168681400314933, 781018023486930, 3621756376540216, 16818597426475822, 78203624439103881

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, -1 + j, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150248 A105871 A150249 * A150251 A150252 A150253

Adjacent sequences: A150247 A150248 A150249 * A150251 A150252 A150253

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved