A148244 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), (-1, 1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 115, 358, 1190, 3930, 13395, 46452, 163827, 581929, 2087571, 7561179, 27583483, 101265250, 374447429, 1393522831, 5210820435, 19569740853, 73828142561, 279648783033, 1062990121685, 4054798167835, 15520276318875, 59584141035987, 229363024568651, 885223757681775, 3425077275385705

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, 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, 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: A148241 A148242 A148243 * A148245 A148246 A148247

Adjacent sequences: A148241 A148242 A148243 * A148245 A148246 A148247

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved