A149221 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), (-1, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 10, 44, 142, 639, 2306, 10609, 40699, 190471, 758754, 3593080, 14686804, 70177775, 292328166, 1406400261, 5943972895, 28744484098, 122895902695, 596740619839, 2575547718451, 12546847069039, 54580650033986, 266592183236824, 1167494384044946, 5714920965467256, 25171907906369844

Offset

0,3

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, -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, 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: A280907 A332233 A149220 * A149222 A264571 A149223

Adjacent sequences: A149218 A149219 A149220 * A149222 A149223 A149224

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved