|
%I #33 Dec 29 2023 14:24:01
%S 0,2,13,48,141,312,652,1160,1978,3106,4775,6826,9803,13328,17904,
%T 23536,30652,38640,48945,60300,74248,89892,108768,128990,153826,
%U 180206,211483,245000,284375,325140,374450,425312,484168,545938,616981,690132,775077,862220
%N Number of regions in a polygon whose boundary consists of n+2 equally space points around a semicircle and n+2 equally spaced points along the diameter (a total of 2n+2 points). See Comments for precise definition.
%C A semicircular polygon with 2n+2 points is created by placing n+2 equally spaced vertices along the semicircle's arc (including the two end vertices). Also place n+2 equally spaced vertices along the diameter (again including the same two end vertices). Now connect every pair of vertices by a straight line segment. The sequence gives the number of regions in the resulting figure.
%H Lars Blomberg, <a href="/A333519/b333519.txt">Table of n, a(n) for n = 0..50</a>
%H Scott R. Shannon, <a href="/A333519/a333519.png">Illustration for n = 2</a>.
%H Scott R. Shannon, <a href="/A333519/a333519_1.png">Illustration for n = 3</a>.
%H Scott R. Shannon, <a href="/A333519/a333519_2.png">Illustration for n = 5</a>.
%H Scott R. Shannon, <a href="/A333519/a333519_3.png">Illustration for n = 10</a>.
%H Scott R. Shannon, <a href="/A333519/a333519_4.png">Illustration for n = 15</a>.
%H Scott R. Shannon, <a href="/A333519/a333519_5.png">Illustration for n = 20</a>.
%Y Cf. A007678, A290865, A255011, A332953, A333282, A334458, A334459.
%K nonn
%O 0,2
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 26 2020
%E a(21) and beyond from _Lars Blomberg_, May 01 2020
|
