A149104 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), (0, 0, -1), (0, 1, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 4, 8, 34, 86, 379, 1109, 4982, 15733, 71949, 241112, 1113488, 3883382, 18098701, 65184740, 305739740, 1128669680, 5322848456, 20056405409, 95002397740, 364024517530, 1730702331804, 6727132522992, 32084009850479, 126237885355729, 603707726422516, 2400683361569746, 11507951243830815

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, j, 1 + k, -1 + n] + aux[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, 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: A149103 A039303 A200159 * A149105 A149106 A149107

Adjacent sequences: A149101 A149102 A149103 * A149105 A149106 A149107

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved