A148705 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, 1), (-1, 1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 7, 23, 74, 250, 896, 3216, 11970, 45118, 172339, 668019, 2611405, 10304201, 40996002, 164121773, 661305741, 2678915088, 10903798400, 44583248139, 183006868153, 753955760694, 3116648090883, 12922549731341, 53732495491218, 224010803310530, 936151633169917, 3921101507663564

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A283109 A339284 A057184 * A148706 A148707 A148708

Adjacent sequences: A148702 A148703 A148704 * A148706 A148707 A148708

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved