A149116 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, 0, 0), (-1, 1, -1), (0, 0, -1), (1, 0, 1)}.

1, 1, 4, 9, 32, 101, 341, 1237, 4356, 16205, 60807, 228181, 885776, 3410715, 13354484, 52830973, 208725094, 836808429, 3358002345, 13541119833, 55050460354, 223785876151, 915759686472, 3759324357789, 15458651365822, 63903321592109, 264471883168233, 1097854258165567, 4571846022733480

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A343547 A151271 A149115 * A149117 A149118 A149119

Adjacent sequences: A149113 A149114 A149115 * A149117 A149118 A149119

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved