A149699 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), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 69, 271, 1143, 4861, 21075, 92001, 405747, 1803693, 8071737, 36317843, 164127723, 744693295, 3390805227, 15488141433, 70940866119, 325734483267, 1498990629875, 6912126391031, 31932076989425, 147766233863115, 684852872148647, 3178630119704709, 14772626581189619, 68739890873719931

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[-1 + i, 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: A339684 A149697 A149698 * A151276 A272743 A149700

Adjacent sequences: A149696 A149697 A149698 * A149700 A149701 A149702

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved