A150139 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, 0, 0), (0, 0, 1), (1, -1, -1), (1, 1, 0)}.

1, 2, 6, 20, 73, 276, 1090, 4416, 18242, 76675, 326150, 1403464, 6091537, 26654395, 117412325, 520268068, 2317636972, 10371361869, 46608781873, 210226515573, 951461046417, 4319309714478, 19663072521834, 89743573185081, 410552491858376, 1882274544712750, 8646913270639666, 39797115879839132

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150137 A150138 A148481 * A052884 A150140 A061396

Adjacent sequences: A150136 A150137 A150138 * A150140 A150141 A150142

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved