A148461 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), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 6, 18, 59, 210, 771, 2934, 11472, 45768, 185861, 766004, 3196617, 13484009, 57423388, 246560056, 1066400837, 4642659695, 20329547786, 89487624762, 395791623498, 1758066178058, 7839884115870, 35087407624114, 157552832011704, 709617265586454, 3205147601026502, 14514588343290364

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, 1 + j, k, -1 + n] + aux[i, 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: A227373 A121320 A148460 * A358251 A002527 A005566

Adjacent sequences: A148458 A148459 A148460 * A148462 A148463 A148464

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved