A151222 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), (0, 0, 1), (0, 1, 1), (1, 1, -1), (1, 1, 1)}

1, 3, 13, 57, 265, 1249, 5985, 28921, 140769, 688451, 3380087, 16643697, 82146741, 406201851, 2011677275, 9975162381, 49514935929, 245999398831, 1223080149815, 6084867581499, 30288917519411, 150841365748097, 751509222633005, 3745439135070101, 18672679963259901, 93117178620432547

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A256939 A005827 A151319 * A349299 A151223 A151224

Adjacent sequences: A151219 A151220 A151221 * A151223 A151224 A151225

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved