A149870 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, -1), (0, 0, 1), (0, 1, 1), (1, -1, -1)}.

1, 2, 5, 13, 42, 138, 482, 1674, 6193, 22905, 87142, 331804, 1297850, 5080751, 20167345, 80358260, 324330890, 1312019214, 5346985706, 21886646737, 90188575104, 372646373051, 1546658755002, 6444345902094, 26956040541657, 113039384227922, 475510150048488, 2006521895619724, 8488924958535221

Offset

0,2

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A088553 A262934 A149869 * A149871 A149872 A149873

Adjacent sequences: A149867 A149868 A149869 * A149871 A149872 A149873

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved