A149322 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, 0, 1)}.

1, 1, 4, 12, 37, 146, 532, 1939, 7867, 30759, 119428, 494439, 1998117, 8031890, 33663606, 138767875, 569739552, 2408265131, 10058849444, 41885466587, 178161102199, 751113795845, 3159201427573, 13502875061936, 57323664729986, 242912678538629, 1042256626250547, 4448498168340005

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, 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: A149320 A362146 A149321 * A149323 A024590 A189499

Adjacent sequences: A149319 A149320 A149321 * A149323 A149324 A149325

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved