A150263 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, 1), (0, 0, 1), (1, -1, 1), (1, 1, 0)}.

1, 2, 6, 22, 88, 362, 1550, 6778, 30104, 135458, 616280, 2825772, 13050732, 60641808, 283188618, 1328339472, 6255474500, 29558166908, 140095615008, 665841903428, 3172346398542, 15148207045422, 72482131975406, 347460312983430, 1668482689041102, 8024617166540062, 38650704248517114, 186413214485517048

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, -1 + 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: A101043 A101046 A363811 * A165534 A165535 A319028

Adjacent sequences: A150260 A150261 A150262 * A150264 A150265 A150266

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved