A151058 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), (0, 1, 0), (1, 0, 0)}

1, 3, 10, 37, 149, 628, 2721, 12059, 54409, 248727, 1148931, 5353961, 25129496, 118650474, 563062546, 2683730824, 12839509507, 61627255892, 296648310192, 1431557251325, 6923863878225, 33554994626662, 162909097363703, 792200806683059, 3857979671452194, 18813130247956668, 91851755076482287

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, j, k, -1 + n] + aux[i, -1 + j, 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: A151057 A063029 A199874 * A044048 A192240 A231894

Adjacent sequences: A151055 A151056 A151057 * A151059 A151060 A151061

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved