A148230 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), (-1, 1, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 13, 33, 123, 366, 1468, 4743, 19935, 68259, 296270, 1059045, 4703653, 17371257, 78488374, 297384019, 1361456225, 5266059738, 24359357814, 95838621697, 447027183728, 1784055744603, 8378335209695, 33846086058778, 159849556940540, 652542059175631, 3096521590494683

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 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, -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: A148227 A148228 A148229 * A227808 A148231 A148232

Adjacent sequences: A148227 A148228 A148229 * A148231 A148232 A148233

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved