A149623 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, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 65, 261, 1107, 4829, 21161, 94699, 427839, 1944321, 8940873, 41227359, 191537351, 893670483, 4185275627, 19689481625, 92872490315, 439533572969, 2085659778339, 9919396974015, 47291966120497, 225887905222775, 1081059581735291, 5182616773275119, 24883937147640411, 119662027002273829

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, -1 + 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, 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: A149621 A149622 A247281 * A149624 A149625 A149626

Adjacent sequences: A149620 A149621 A149622 * A149624 A149625 A149626

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved