A149175 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, 0, -1), (1, -1, 0), (1, 1, 0)}

1, 1, 4, 10, 35, 117, 429, 1563, 6023, 23289, 92152, 369488, 1502119, 6160145, 25528852, 106682938, 448960587, 1901408027, 8104762740, 34722538926, 149465829383, 646360473228, 2806706370121, 12231645222422, 53492893993153, 234717283187637, 1032901850100970, 4557956790155818, 20167098103048672

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, 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: A339845 A234009 A198324 * A149176 A059710 A149177

Adjacent sequences: A149172 A149173 A149174 * A149176 A149177 A149178

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved