A122226 Length of the longest possible self-avoiding path on the 2-dimensional triangular lattice such that the path fits into a circle of diameter n.

1, 7, 10, 19, 24, 37, 48, 61

Offset: 1

Author

Hugo Pfoertner, Sep 25 2006

Keywords

• hard
• more
• nonn

Comments

The path may be open or closed. For larger n several solutions with the same number of segments exist.

It is conjectured that the sequence is identical with A125852 for all n>1. That means that it is always possible to find an Hamiltonian cycle on the maximum possible number of lattice points that can be covered by circular disks of diameter >=2. For the given additional terms it was easily possible to construct such closed paths by hand, using the lattice subset found by the exhaustive search for A125852. See the examples at the end of the linked pdf file a122226.pdf that were all generated without using a program. - Hugo Pfoertner, Jan 12 2007

Links

• Hugo Pfoertner, Examples of compact self avoiding paths on a triangular lattice.

Crossrefs

Cf. A003215, A004016; A125852 gives upper bounds for a(n).

Cf. A122223, A122224.

Extensions

a(7) and a(8) from Hugo Pfoertner, Dec 11 2006