The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #57 Sep 26 2024 12:57:25
%S 3,12,22
%N Maximum number of edges in a simple polygon that is the union of n triangles.
%C By an explicit construction, a(n) >= 10n-8 for all n >= 2. a(4) >= 33, a(5) >= 44.
%H Math Stackexchange, <a href="https://math.stackexchange.com/questions/4724701/if-a-union-of-n-triangles-is-a-simple-m-gon-find-the-maximum-of-m">If a union of n triangles is a simple M-gon, find the maximum of M</a>.
%H Giedrius Alkauskas, <a href="/A375986/a375986_1.jpg">Three configurations</a>
%H Giedrius Alkauskas, <a href="/A375986/a375986.png">Construction</a> which shows that a(n) >= 10*n-8.
%e For n = 1, one has three vertices of a single triangle.
%e For n = 2 the example is provided by a configuration that is the star of David.
%K nonn,bref
%O 1,1
%A _Giedrius Alkauskas_, Sep 07 2024