A151206 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), (0, 1, 0), (1, 0, 1), (1, 1, 1)}.

1, 3, 12, 54, 250, 1180, 5670, 27452, 133915, 656402, 3228231, 15923764, 78713040, 389752400, 1932628118, 9593741055, 47669074257, 237042050552, 1179494090334, 5872303954319, 29250041433290, 145754081231068, 726554355645339, 3622829639676563, 18069395625479960, 90144892416527275

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, j, -1 + k, -1 + n] + aux[i, -1 + 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: A123348 A151204 A151205 * A151207 A083881 A151208

Adjacent sequences: A151203 A151204 A151205 * A151207 A151208 A151209

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved