A149475 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, 0, 1), (-1, 1, 0), (0, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 56, 226, 992, 4379, 19858, 90896, 421880, 1972067, 9292868, 44031800, 209706374, 1002851646, 4813287969, 23172425977, 111861209159, 541258139896, 2624423722255, 12748621918657, 62030817232581, 302268078881713, 1474874579650713, 7205109160293116, 35237202124383216, 172502683686676076

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A365854 A188205 A149474 * A149476 A121076 A121070

Adjacent sequences: A149472 A149473 A149474 * A149476 A149477 A149478

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved