A150020 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), (0, 1, 0), (1, 0, 1)}.

1, 2, 5, 18, 67, 242, 977, 4046, 16328, 69645, 300988, 1277990, 5613890, 24861140, 108667372, 486175793, 2187282271, 9740962302, 44128325356, 200720461844, 905597752795, 4139718039504, 18981995857907, 86462331795136, 397944480795058, 1835973674030347, 8423840262046013, 38977707542636047

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A150018 A150019 A005753 * A144721 A150021 A150022

Adjacent sequences: A150017 A150018 A150019 * A150021 A150022 A150023

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved