A148883 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), (0, 1, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 3, 8, 30, 97, 380, 1432, 5730, 23215, 95928, 402954, 1715098, 7372699, 32074694, 140435319, 620668756, 2758615766, 12342172004, 55515576430, 250924509615, 1139470870886, 5195091511618, 23776892239251, 109201412722348, 503132997084698, 2325166974024119, 10774845621104857, 50061102370626852

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A148880 A148881 A148882 * A148884 A148885 A148886

Adjacent sequences: A148880 A148881 A148882 * A148884 A148885 A148886

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved