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Search: id:A122226
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| A122226 |
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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. |
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+0
7
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OFFSET
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1,2
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COMMENT
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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 (hugo(AT)pfoertner.org), Jan 12 2007
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LINKS
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Hugo Pfoertner, Examples of compact self avoiding paths on a triangular lattice.
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CROSSREFS
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Cf. A003215, A004016; A125852 gives upper bounds for a(n).
Cf. A122223, A122224.
Sequence in context: A124187 A118420 A038211 this_sequence A064210 A097634 A120312
Adjacent sequences: A122223 A122224 A122225 this_sequence A122227 A122228 A122229
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KEYWORD
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hard,more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 25 2006
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EXTENSIONS
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a(7) and a(8) from Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 11 2006
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