A151205 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, 0), (0, 1, 0), (1, 0, 1), (1, 1, -1), (1, 1, 1)}

1, 3, 12, 54, 249, 1177, 5636, 27249, 132741, 649642, 3191756, 15726012, 77663557, 384258080, 1903995456, 9445840534, 46908432474, 233146909282, 1159624911004, 5771215398000, 28737003810563, 143155655455776, 713415855046229, 3556494722952293, 17734887091858891, 88459818213824273

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, 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: A282901 A123348 A151204 * A151206 A151207 A083881

Adjacent sequences: A151202 A151203 A151204 * A151206 A151207 A151208

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved