A151124 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, 1, -1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}.

1, 3, 11, 45, 194, 870, 3993, 18631, 88068, 420149, 2019374, 9763410, 47425833, 231270952, 1131400826, 5549719306, 27284114986, 134394443468, 663082316282, 3276197809494, 16207136789740, 80261675763645, 397848536171198, 1973720814240814, 9798743484589656, 48678325970474082, 241963833919074855

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + 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: A142876 A151122 A151123 * A151125 A151126 A151127

Adjacent sequences: A151121 A151122 A151123 * A151125 A151126 A151127

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved