A149402 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, 0, 0), (-1, 0, 1), (1, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 51, 190, 842, 3431, 15654, 67330, 312993, 1392581, 6555426, 29833990, 141757524, 655762121, 3137841689, 14692467913, 70689773071, 334087875481, 1614441359873, 7686127259903, 37274642271835, 178505613655953, 868232040289333, 4177913803818686, 20371131449476345, 98416106111044095

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[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149399 A149400 A149401 * A045906 A025282 A303392

Adjacent sequences: A149399 A149400 A149401 * A149403 A149404 A149405

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved