A148348 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, 0), (1, -1, 1), (1, 0, 1)}.

1, 1, 2, 5, 15, 40, 134, 415, 1432, 4780, 17264, 59682, 222798, 796307, 3025348, 11120761, 42897182, 160722169, 628867869, 2392267677, 9461745050, 36488189918, 145551730058, 567697425815, 2282095807142, 8983974127676, 36359390767732, 144308356382112, 587373410447617, 2348146997244465

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A148347 A309299 A151260 * A148349 A076865 A190140

Adjacent sequences: A148345 A148346 A148347 * A148349 A148350 A148351

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved