A148891 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, 1), (1, -1, -1), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 8, 31, 99, 411, 1512, 6497, 25717, 113560, 470615, 2119435, 9069212, 41430503, 181543837, 838373030, 3740867568, 17423551011, 78857867841, 369838661718, 1693046404678, 7985762164083, 36898943558246, 174881314068075, 814316512661987, 3875201367249076, 18161941728609720, 86733820305600697

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + 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: A119838 A148889 A148890 * A148892 A148893 A148894

Adjacent sequences: A148888 A148889 A148890 * A148892 A148893 A148894

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved