A149262 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, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 4, 11, 40, 124, 474, 1599, 6214, 21790, 85368, 306948, 1209606, 4426724, 17512502, 64916857, 257475442, 963710264, 3829460462, 14442356656, 57468053150, 218058093974, 868578080482, 3312203437546, 13203816362654, 50560048999552, 201677765851598, 774971022480474, 3092771736311868

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A050911 A149260 A149261 * A149263 A149264 A264331

Adjacent sequences: A149259 A149260 A149261 * A149263 A149264 A149265

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved