A148887 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, 0, 0), (0, -1, 1), (0, 0, 1), (0, 1, -1), (1, 1, -1)}.

1, 1, 3, 8, 30, 102, 399, 1549, 6331, 26197, 111058, 476943, 2078542, 9150328, 40704579, 182483318, 824427887, 3747916247, 17138403170, 78769757858, 363711035059, 1686399296077, 7848812615643, 36655434057447, 171727138976925, 806840773536620, 3800922650135408, 17949434069870888, 84956189865687628

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148884 A148885 A148886 * A221537 A148888 A151440

Adjacent sequences: A148884 A148885 A148886 * A148888 A148889 A148890

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved