A148970 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), (0, -1, 1), (0, 1, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 3, 9, 31, 110, 413, 1586, 6338, 25587, 105668, 441742, 1869009, 7988512, 34452295, 149655845, 654683791, 2880468569, 12740749488, 56624461023, 252720799653, 1132300360975, 5091068882597, 22963600275420, 103884299000600, 471227976010791, 2142846539057306, 9766818079951710, 44610952963232566

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + 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: A148969 A112566 A128082 * A151459 A151033 A047012

Adjacent sequences: A148967 A148968 A148969 * A148971 A148972 A148973

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved