0,6

a(n) counts the topologically distinct planar configurations of n unbounded curves such that each curve crosses each other curve at exactly one point and no two intersection points coincide. For n<8, a(n) is identical to A090338(n), where the curves must be straight line segments. But at n=8, we find a(n) includes three configurations that cannot be drawn with straight line segments. The qualification "unbounded" disallows configurations that have an endpoint within an area enclosed by other curves. As in A090338(n), configurations related by mirror symmetry are not counted as distinct.

Jon Wild and Laurence Reeves, One of the three configurations for n=8

See illustration for one of the three configurations for n=8 that is not drawable with straight lines and so does not appear in A090338. No further intersections between curves, beyond the ones shown, occur outside the visible portion of the plane.

Cf. A090338.

Sequence in context: A062266 A159604 A090338 this_sequence A078810 A114074 A075337

Adjacent sequences: A090336 A090337 A090338 this_sequence A090340 A090341 A090342

more,nonn

Jon Wild (wild(AT)music.mcgill.ca) and Laurence Reeves (l(AT)bergbland.info), Jan 27 2004