A149700 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, 0), (0, -1, 1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 69, 277, 1175, 4991, 21707, 95019, 420485, 1872483, 8392935, 37803043, 171044287, 776817969, 3540037073, 16179841235, 74148407971, 340610270961, 1568026396723, 7232622699345, 33420763418641, 154684729671295, 717026052876837, 3328341395275273, 15469743336597625, 71988145309748133

Offset

0,3

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, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149699 A151276 A272743 * A149701 A149702 A273331

Adjacent sequences: A149697 A149698 A149699 * A149701 A149702 A149703

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved