A148926 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, 0), (0, 1, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 9, 27, 93, 335, 1193, 4499, 17397, 66791, 264641, 1065531, 4268397, 17449359, 72138297, 297057699, 1240941285, 5227368119, 21948770097, 93160744715, 397989148381, 1695548287455, 7285282665385, 31466403150451, 135579832581973, 588237646174215, 2563188668607393, 11144626999776731

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A217639 A328080 A148925 * A146573 A148927 A148928

Adjacent sequences: A148923 A148924 A148925 * A148927 A148928 A148929

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved