A149237 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, 0, 1), (0, 0, -1), (1, 1, 1)}.

1, 1, 4, 11, 36, 114, 392, 1319, 4572, 15806, 55800, 196414, 698936, 2488452, 8935696, 32093615, 115879740, 418874694, 1520690456, 5525783450, 20139817064, 73488506268, 268834264688, 984430431638, 3611768138328, 13264952716588, 48798930171056, 179686392437468, 662521532267376, 2444965457206408

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A212910 A339034 A114248 * A054577 A206687 A106640

Adjacent sequences: A149234 A149235 A149236 * A149238 A149239 A149240

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved