A122226 - OEIS

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

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OFFSET

1,2

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

Table of n, a(n) for n=1..8.

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.

Sequence in context: A118420 A196939 A038211 * A240791 A064210 A249942

Adjacent sequences: A122223 A122224 A122225 * A122227 A122228 A122229

KEYWORD

hard,more,nonn

AUTHOR

Hugo Pfoertner, Sep 25 2006

EXTENSIONS

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

STATUS

approved