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A301894 Number of real lines on a smooth real cubic surface. 0


%S 3,7,15,27

%N Number of real lines on a smooth real cubic surface.

%C Schläfli proved that a smooth real cubic surface contains either 3, 7, 15, or 27 straight lines.

%H D. Schläfli, <a href="http://rstl.royalsocietypublishing.org/content/153/193">On the distribution of surfaces of the third order into species, in reference to the absence or presence of singular points, and the reality of their lines</a>, Philosophical Transactions of the Royal Society of London, 153 (1863), 193-241.

%H Kirsten Wickelgren, <a href="http://www.ams.org/journals/notices/201804/rnoti-p401.pdf">An Arithmetic Count of the Lines on a Smooth Cubic Surface</a>, AMS Notices, 65 (2018), 404-405.

%F a(n) = A097080(n) = 2*n^2 - 2*n + 3 for n = 1, 2, 3, 4.

%e The number of lines on a smooth complex cubic surface is a(4) = A027363(2) = A238370(1) = 27.

%Y Cf. A027363, A238370.

%K nonn,fini,full

%O 1,1

%A _Jonathan Sondow_, Mar 28 2018

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Last modified June 17 05:08 EDT 2021. Contains 345080 sequences. (Running on oeis4.)