A150883 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, 0, 1), (0, 1, -1), (1, -1, 1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 33, 149, 689, 3259, 15596, 75353, 366486, 1791533, 8791782, 43276756, 213542743, 1055751847, 5227922739, 25921772174, 128668445966, 639255561410, 3178413212779, 15813550746417, 78720978575891, 392066434170623, 1953478763295965, 9736748070491251, 48546225260336401, 242112066053535433

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[-1 + i, 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, -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: A150881 A053817 A150882 * A150884 A150885 A150886

Adjacent sequences: A150880 A150881 A150882 * A150884 A150885 A150886

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved