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%I #20 May 21 2022 19:39:35
%S 1,1,1,1,1,6,43,922,38612,3113660
%N Number of full curvilinear flups with n curves.
%C 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.
%C 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.
%H Jean-Luc Baril, Céline Moreira Dos Santos, <a href="http://jl.baril.u-bourgogne.fr/pancake.pdf">Pizza-cutter's problem and Hamiltonian path</a>, Mathematics Magazine (2019) Vol. 88, No. 1, 1-9. [This paper appears to say that A090338(9) = 3111341. I believe this is an error, and 3111341 refers to the ninth term of the present sequence. - _N. J. A. Sloane_, Feb 15 2021]
%H Finschi, Lukas, <a href="http://dx.doi.org/10.3929/ethz-a-004255224">A graph theoretical approach for reconstruction and generation of oriented matroids</a>, (2001). Diss., Mathematische Wissenschaften ETH Zürich, Nr. 14335, 2001. See table on page 165.
%H Jon Wild and Laurence Reeves, <a href="/A090339/a090339.gif">One of the three configurations for n=8 that cannot be drawn with straight lines</a>
%e 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.
%Y Cf. A090338.
%K more,nonn
%O 0,6
%A _Jon Wild_ and _Laurence Reeves_, Jan 27 2004
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