A149103 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, 0, 1), (1, 1, -1)}.

1, 1, 4, 8, 33, 96, 365, 1256, 4738, 17499, 67405, 257304, 1010718, 3952610, 15734129, 62646598, 252260108, 1017085209, 4137530712, 16846884916, 69094767176, 283689835603, 1171287775035, 4842352230909, 20109490407136, 83614450595364, 348992273146901, 1458301368654140, 6113124302597799

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, 1 + k, -1 + n] + aux[-1 + i, 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: A149100 A149101 A149102 * A039303 A200159 A149104

Adjacent sequences: A149100 A149101 A149102 * A149104 A149105 A149106

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved