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a(n) = number of regions in the configuration A290447(n).
10

%I #17 Mar 07 2020 11:26:00

%S 0,1,3,7,15,30,56,98,161,250,370,536,748,1027,1379,1807,2320,2954,

%T 3702,4604,5652,6852,8239,9858,11683,13748,16086,18700,21604,24887,

%U 28471,32491,36907,41751,47080,52876,59105,65965,73440,81521,90176

%N a(n) = number of regions in the configuration A290447(n).

%H David Applegate, <a href="/A290865/b290865.txt">Table of n, a(n) for n = 1..100</a>

%H M. F. Hasler, <a href="/A290447/a290447.html">Interactive web page for drawing the illustration for a(n).</a>

%H N. J. A. Sloane (in collaboration with Scott R. Shannon), <a href="/A331452/a331452.pdf">Art and Sequences</a>, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.

%e With 3 points, there are 3 semicircles above the baseline, which bound a(3) = 3 regions. With 4 points, there are 6 semicircles, defining 7 regions (use the Halser webpage with n = 3 and 4). - _N. J. A. Sloane_, Aug 12 2017

%Y Cf. A290447, A290866, A290867, A332723 (number of regions with k edges).

%Y See also A290876.

%K nonn

%O 1,3

%A _David Applegate_, Aug 12 2017