A148159 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, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 30, 101, 325, 1173, 4129, 15600, 57991, 227819, 882158, 3556595, 14196649, 58341251, 237985861, 994094162, 4126639959, 17456975753, 73516604930, 314208829825, 1338355571447, 5771924502800, 24822352236154, 107856520063495, 467688123042216, 2045200218407310, 8929933841268928

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 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: A215460 A339225 A148158 * A275310 A102814 A193059

Adjacent sequences: A148156 A148157 A148158 * A148160 A148161 A148162

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved