A149837 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, -1), (-1, -1, 0), (0, 1, 0), (1, 0, 1)}.

1, 2, 4, 12, 36, 100, 324, 1052, 3228, 10852, 36532, 117676, 404364, 1390516, 4610980, 16077660, 56078812, 189603652, 668095892, 2354323852, 8071935148, 28669742292, 101819683204, 352800887100, 1260929362940, 4505714683748, 15742066776692, 56548206097260, 203073342063308, 714263158415348, 2576510962881380

Offset

0,2

Links

Table of n, a(n) for n=0..30.

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, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A325255 A084716 A241208 * A149838 A192236 A149839

Adjacent sequences: A149834 A149835 A149836 * A149838 A149839 A149840

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved