A150917 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, 0), (-1, 1, -1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 32, 149, 627, 2941, 13209, 62687, 290048, 1389629, 6540502, 31550069, 150162266, 727976787, 3492066553, 16992947285, 81987733624, 400130137529, 1939146072783, 9485747916278, 46132187730314, 226093194349279, 1102681312996272, 5412743934820356, 26460130323088936, 130058214498923137

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, -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] + aux[1 + i, 1 + 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: A150914 A150915 A150916 * A150918 A150919 A150920

Adjacent sequences: A150914 A150915 A150916 * A150918 A150919 A150920

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved