A148310 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), (-1, 0, 0), (-1, 1, 0), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 5, 14, 37, 116, 360, 1153, 3817, 12954, 44046, 154992, 545891, 1945476, 7064170, 25693848, 94083579, 350376440, 1301899782, 4869681054, 18458415299, 69773046856, 265110681738, 1019157361190, 3903891771434, 15021935369908, 58394707450808, 226123722643103, 879041601998166, 3448592905706929

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A148307 A148308 A148309 * A148311 A148312 A148313

Adjacent sequences: A148307 A148308 A148309 * A148311 A148312 A148313

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved