A149100 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), (0, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 8, 33, 96, 356, 1247, 4571, 17184, 65009, 248797, 973981, 3792464, 15064338, 59942711, 239916910, 969858096, 3922559131, 15980739490, 65382849875, 268024851468, 1105180616622, 4564678257229, 18914827942473, 78657929701182, 327546334235796, 1368466497881361, 5728666877270046

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[i, -1 + j, 1 + k, -1 + n] + aux[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: A149097 A149098 A149099 * A149101 A149102 A149103

Adjacent sequences: A149097 A149098 A149099 * A149101 A149102 A149103

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved