A151181 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), (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}

1, 3, 12, 50, 230, 1059, 5043, 24073, 116650, 566294, 2770564, 13575457, 66809023, 329196128, 1626369177, 8042962723, 39842574055, 197525771175, 980382103175, 4869026293964, 24201218678644, 120351728434595, 598854576465375, 2981035269045935, 14845798328053850, 73957590749549226, 368560458686376624

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + 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: A105479 A151180 A268650 * A094601 A242155 A009024

Adjacent sequences: A151178 A151179 A151180 * A151182 A151183 A151184

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved