

A333642


Number of regions in a polygon whose boundary consists of n+2 equally space points around a semicircle and three equally spaced points along the diameter (a total of n+3 points). See Comments for precise definition.


5



2, 8, 20, 43, 80, 139, 224, 324, 510, 730, 992, 1373, 1820, 2187, 3040, 3844, 4720, 5916, 7220, 8498, 10472, 12463, 14570, 17278, 20150, 23130, 26964, 30961, 34688, 40265, 45632, 51138, 57970, 65008, 72322, 80979, 89984, 99197, 110240, 121570, 132896, 146818
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OFFSET

1,1


COMMENTS

A semicircular polygon with n+3 points is created by placing n+2 equally spaced vertices along the semicircle's arc (including the two end vertices). Also place three equally spaced vertices along the diameter; these are the same two end vertices plus one dividing the diameter. Now connect every pair of vertices by a straight line segment. The sequence gives the number of regions in the resulting figure.


LINKS

Lars Blomberg, Table of n, a(n) for n = 1..100
Scott R. Shannon, Illustration for n = 2.
Scott R. Shannon, Illustration for n = 3.
Scott R. Shannon, Illustration for n = 4.
Scott R. Shannon, Illustration for n = 5.
Scott R. Shannon, Illustration for n = 7.
Scott R. Shannon, Illustration for n = 10.
Scott R. Shannon, Illustration for n = 12.
Scott R. Shannon, Illustration for n = 15.
Scott R. Shannon, Illustration for n = 17.
Scott R. Shannon, Illustration for n = 19.
Scott R. Shannon, Illustration for n = 20.
Scott R. Shannon, Illustration for n = 10 with random distancebased coloring.
Scott R. Shannon, Illustration for n = 15 with random distancebased coloring.
Scott R. Shannon, Illustration for n = 19 with random distancebased coloring.
Scott R. Shannon, Illustration for n = 20 with random distancebased coloring.
Wikipedia, Semicircle.


CROSSREFS

Cf. A330914 (ngons), A330911 (edges), A330913 (vertices), A333643, A333519, A007678, A290865, A092867, A331452, A331929, A331931.
Sequence in context: A072250 A220908 A057566 * A009303 A096586 A165751
Adjacent sequences: A333639 A333640 A333641 * A333643 A333644 A333645


KEYWORD

nonn


AUTHOR

Scott R. Shannon and N. J. A. Sloane, Mar 31 2020


EXTENSIONS

a(21) and beyond from Lars Blomberg, May 03 2020


STATUS

approved



