A149851 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, -1, 1), (-1, 0, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 4, 14, 46, 154, 578, 2056, 7734, 29832, 113786, 448286, 1762158, 6982215, 28034055, 112599212, 456160196, 1855679003, 7575193160, 31073949234, 127882427241, 528025970306, 2186615978962, 9081877366235, 37801377197439, 157763676455239, 659823092941944, 2764674164214323

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A149849 A149850 A255502 * A149852 A263740 A005437

Adjacent sequences: A149848 A149849 A149850 * A149852 A149853 A149854

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved