0,6

The full n-flups are the topologically distinct planar configurations of n straight line segments such that each segment crosses each other segment at exactly one intersection point; no two intersection points coincide; and no intersection point coincides with a segment's endpoint. a(n) also gives the number of distinct ways to divide a cake with n vertical cuts such that the maximal number of pieces results (see A000125).

Jon Wild and Laurence Reeves, Illustration of a(5)

See illustration of a(5), the full pentaflups. Of the six, the last shown does not have reflectional symmetry, but we do not count its mirror image as distinct. All six are drawn with lines at equally-spaced angles; it is usually (but not always) possible to achieve this (41 out of 43 of the full 6-flups, for example, have equi-angled drawings)

Cf. A000125, A090339.

Sequence in context: A090010 A062266 A159604 this_sequence A090339 A078810 A114074

Adjacent sequences: A090335 A090336 A090337 this_sequence A090339 A090340 A090341

more,nonn,hard

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