A148173 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, 0)}.

1, 1, 2, 4, 12, 27, 84, 224, 712, 2006, 6662, 19530, 66075, 200135, 685767, 2140539, 7392879, 23476786, 82121415, 264696045, 931959429, 3044412236, 10778956363, 35653064603, 126785519562, 422881232793, 1512592426073, 5085508697560, 18251871593345, 61808600080037, 222558094522429, 758833465387375

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 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: A242536 A027132 A148172 * A148174 A232218 A292065

Adjacent sequences: A148170 A148171 A148172 * A148174 A148175 A148176

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved