A149385 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), (-1, 0, 1), (0, 1, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 12, 48, 188, 790, 3373, 14775, 65711, 296183, 1349263, 6200429, 28702895, 133696901, 626086696, 2945367102, 13911989913, 65943630939, 313555617506, 1495083989143, 7146639957156, 34238554950923, 164366582896944, 790525990606840, 3808495347158545, 18376542286319936, 88795969816237845

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A108508 A019309 A056632 * A092898 A110594 A151483

Adjacent sequences: A149382 A149383 A149384 * A149386 A149387 A149388

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved