A149963 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, 1, 1), (0, 1, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 16, 54, 191, 708, 2707, 10567, 41958, 169489, 693112, 2862188, 11938097, 50203658, 212547996, 905664031, 3881507300, 16718531338, 72339810648, 314353186474, 1371267039900, 6002587243116, 26362181952163, 116128273001736, 512978800860645, 2271923020590513, 10086706189351192

Offset

0,2

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, j, 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] + 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: A149961 A141754 A149962 * A149964 A148399 A149965

Adjacent sequences: A149960 A149961 A149962 * A149964 A149965 A149966

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved