A148975 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, 32, 107, 406, 1543, 6090, 24146, 98643, 406416, 1695798, 7137445, 30371510, 130114585, 561109001, 2434945076, 10628079754, 46605896147, 205271832088, 907951122880, 4031163410729, 17957103579357, 80244610168837, 359663685481550, 1616386069956481, 7282307288193565, 32886927632112087

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: A148972 A148973 A148974 * A148976 A148977 A202143

Adjacent sequences: A148972 A148973 A148974 * A148976 A148977 A148978

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved