A149893 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), (0, 1, 0), (1, 0, -1)}.

1, 2, 5, 14, 45, 155, 553, 2049, 7832, 30577, 121584, 491526, 2013629, 8342993, 34924457, 147498787, 627773947, 2690792993, 11606230826, 50343025311, 219495098281, 961494709417, 4229766776044, 18680738398857, 82803011897563, 368252104098982, 1642825151126609, 7350053482843933

Offset

0,2

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, j, 1 + k, -1 + n] + aux[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: A149890 A149891 A149892 * A149894 A030126 A081444

Adjacent sequences: A149890 A149891 A149892 * A149894 A149895 A149896

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved