cp's OEIS Frontend

This is the finite list of 32 counts of smaller cubes that a cube cannot be subdivided into.

It is not proven that the last couple of terms belong to this sequence - see Hickerson link.

Note that cubes themselves are not on the list.

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 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.

This is in the affine plane, rather than the projective plane, so two lines are either parallel or meet in one point.

Here we only consider arrangements of n lines in "general position", with every two lines meeting in one point and every intersection point lying on exactly two lines. See A241600 for the general case.

Two arrangements are considered the same if the lines in each arrangement can be numbered from 1 to n in such a way that, on each line, the order of crossings with the other lines is the same in the two arrangements. In particular, turning over the whole arrangement is allowed. (This does not imply that one arrangement can be continuously changed to the other (possibly after turning over) while keeping all lines straight, without changing the multiplicity of intersection points, and without a line passing through an intersection point, see the papers by Suvorov, Jaggi et al., Richter-Gebert, and Tsukamoto.)

Old name was "Number of full n-flups". The full n-flups are the topologically distinct planar configurations of n straight lines such that each line crosses each other line at exactly one intersection point and no two intersection points coincide.

Also, the number of distinct ways to divide a pancake with n straight cuts that result in the maximal number of pieces (see A000124, A000125).