A149996 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, 1, -1), (-1, 1, 1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 59, 214, 803, 3112, 12175, 48204, 193547, 783625, 3192053, 13089520, 54000289, 223719067, 930532505, 3885596256, 16278334661, 68386305015, 288067637489, 1216459217496, 5148025687209, 21829791198372, 92742834232835, 394696063533898, 1682409396500289, 7182037203747231

Offset

0,2

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, 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, -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: A148413 A149994 A149995 * A149997 A149998 A149999

Adjacent sequences: A149993 A149994 A149995 * A149997 A149998 A149999

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved