A148179 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), (-1, 1, -1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 12, 28, 91, 247, 877, 2567, 9614, 29933, 116257, 378638, 1514149, 5106545, 20883108, 72470751, 301746422, 1072034351, 4530557200, 16417140603, 70249343442, 258899615482, 1119612561509, 4187069695975, 18272653982056, 69215461294551, 304463707987332, 1166400842622832, 5166572419820000

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[-1 + i, j, 1 + k, -1 + n] + aux[1 + 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: A148177 A080876 A148178 * A148180 A148181 A331687

Adjacent sequences: A148176 A148177 A148178 * A148180 A148181 A148182

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved