A149134 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), (-1, 0, 1), (0, -1, 1), (1, 1, 0)}.

1, 1, 4, 9, 34, 110, 386, 1453, 5156, 20174, 74994, 293878, 1140716, 4472826, 17816014, 70468423, 283996688, 1137686308, 4610999048, 18688574722, 76099976154, 311108960790, 1273421789480, 5237156169806, 21550990170296, 89026276118776, 368136777403556, 1526411900767346, 6338474045523214

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, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A149131 A149132 A149133 * A149135 A149136 A358411

Adjacent sequences: A149131 A149132 A149133 * A149135 A149136 A149137

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved