A148393 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, 0), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 16, 52, 183, 664, 2449, 9362, 36633, 145270, 586439, 2398743, 9905045, 41348528, 174110004, 738361192, 3154440182, 13559465468, 58601967026, 254620276210, 1111404780914, 4871741807378, 21440930894794, 94702771111481, 419700986590893, 1865899431263205, 8319362447227408

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A148392 A149956 A149957 * A148394 A291685 A268571

Adjacent sequences: A148390 A148391 A148392 * A148394 A148395 A148396

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved