A150239 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, -1, 1), (0, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 6, 22, 83, 332, 1368, 5795, 25056, 109728, 487127, 2183634, 9876620, 45013605, 206392540, 951751965, 4410088770, 20525178508, 95902782437, 449629623563, 2114703239664, 9974225860031, 47168047500241, 223591715338331, 1062195156262639, 5056231328357786, 24113430736934678, 115198155735233773

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A150237 A122449 A150238 * A150240 A150241 A150242

Adjacent sequences: A150236 A150237 A150238 * A150240 A150241 A150242

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved