A273280 Number of topologically-distinct slicings of a square by n lines in general position.

1, 1, 2, 5, 19, 129, 1806

Offset

0,3

Comments

Similar to A272906, but for squares instead of circles. Here a square is cut by a set of n lines in general position, i.e., there are no parallel lines nor 3 lines concurrent in a point. For every slicing we build a graph which has one node per region and an edge between two nodes if the corresponding regions are adjacent. This sequence gives the number of distinct graphs up to isomorphism. See illustration in Links.

Current terms have been obtained by generating about 10^8 randomized slicings: it would be better to confirm these values by means of a systematic enumeration.

This sequence differs from A272906 starting from a(5). Indeed, in the circle, the slicing produced by 5 chords arranged like an inscribed pentagon corresponds to a 5-star graph, which is impossible to attain in the square, since there are only 4 corners the lines can cut.

Links

Table of n, a(n) for n=0..6.

Giovanni Resta, Illustration of a(3)-a(5)

Crossrefs

Cf. A272906, A090338.

Sequence in context: A342435 A341036 A365435 * A272906 A054926 A002786

Adjacent sequences: A273277 A273278 A273279 * A273281 A273282 A273283

Keyword

nonn,more

Author

Giovanni Resta, May 19 2016

Status

approved