A150170 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, 1, -1), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 20, 76, 299, 1236, 5232, 22675, 99949, 447039, 2022251, 9240139, 42562644, 197455398, 921601823, 4324286790, 20384608216, 96487680824, 458373282220, 2184643468897, 10442572405289, 50046778230613, 240424223189811, 1157493695441397, 5583603936153083, 26983173704954285, 130613769257910958

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + 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: A263901 A150169 A083691 * A150171 A263902 A150172

Adjacent sequences: A150167 A150168 A150169 * A150171 A150172 A150173

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved