A150152 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, 0, 1), (0, 1, 1), (1, 1, -1)}.

1, 2, 6, 20, 74, 280, 1114, 4524, 18754, 79016, 337266, 1454404, 6331178, 27766808, 122588426, 544370788, 2429515266, 10891604192, 49023258306, 221441740324, 1003506751162, 4560895150064, 20784202154778, 94945262532860, 434691743439650, 1994255963947296, 9166518865113490, 42207624317954204

Offset

0,2

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A150150 A150151 A361753 * A107284 A211966 A150153

Adjacent sequences: A150149 A150150 A150151 * A150153 A150154 A150155

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved