A330911 -id:A330911 - cp's OEIS frontend

A333642 Number of regions in a polygon whose boundary consists of n+2 equally spaced points around a semicircle and three equally spaced points along the diameter (a total of n+3 points). See Comments for precise definition.

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

Offset: 1

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

nonn

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.

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 distance-based coloring.
Scott R. Shannon, Illustration for n = 15 with random distance-based coloring.
Scott R. Shannon, Illustration for n = 19 with random distance-based coloring.
Scott R. Shannon, Illustration for n = 20 with random distance-based coloring.
Wikipedia, Semicircle.

Cf. A330914 (n-gons), A330911 (edges), A330913 (vertices), A333643, A333519, A007678, A290865, A092867, A331452, A331929, A331931.

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

A330913 The number of vertices formed by straight line segments mutually connecting all vertices of a semicircular polygon defined in A333642.

Original entry on oeis.org

4, 8, 16, 34, 63, 113, 185, 253, 438, 638, 854, 1228, 1641, 1825, 2783, 3543, 4304, 5508, 6748, 7745, 9859, 11773, 13653, 16409, 19178, 21838, 25770, 29648, 32696, 38683, 43899, 48903, 55916, 62784, 69604, 78378, 87175, 95699, 106993, 118093, 128431, 142838

Offset: 1

Scott R. Shannon and N. J. A. Sloane, May 02 2020

nonn

See A333642 for a precise definition of the polygon and images.

Lars Blomberg, Table of n, a(n) for n = 1..100

Cf. A333642 (regions), A330911 (edges), A330914 (n-gons), A331453, A333026, A006561.

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

A330914 Irregular table read by rows: Take a semicircular polygon with all vertices mutually connected by straight line segments, as in A333642. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

Original entry on oeis.org

2, 7, 1, 16, 4, 30, 10, 3, 52, 20, 8, 79, 47, 10, 3, 116, 86, 18, 4, 168, 145, 9, 2, 234, 212, 52, 12, 319, 312, 80, 17, 2, 430, 446, 96, 18, 2, 551, 616, 173, 28, 5, 730, 792, 248, 44, 6, 960, 1035, 167, 25, 1148, 1384, 422, 66, 20

Offset: 1

Scott R. Shannon and N. J. A. Sloane, May 02 2020

See A333642 for a precise definition of the polygon and images.

			Table begins:
2;
7,1;
16,4;
30,10,3;
52,20,8;
79,47,10,3;
116,86,18,4;
168,145,9,2;
234,212,52,12;
319,312,80,17,2;
430,446,96,18,2;
551,616,173,28,5;
730,792,248,44,6;
960,1035,167,25;
1148,1384,422,66,20;
1427,1745,552,108,12;
1784,2154,648,120,14;
2179,2618,927,164,27,1
2652,3200,1088,244,36;
3237,3842,1170,218,26,3,2;

Cf. A333642 (regions), A330911 (edges), A330913 (vertices), A331932, A333025, A331451.

cp's OEIS Frontend

A333642 Number of regions in a polygon whose boundary consists of n+2 equally spaced points around a semicircle and three equally spaced points along the diameter (a total of n+3 points). See Comments for precise definition.

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A330913 The number of vertices formed by straight line segments mutually connecting all vertices of a semicircular polygon defined in A333642.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A330914 Irregular table read by rows: Take a semicircular polygon with all vertices mutually connected by straight line segments, as in A333642. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

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Author

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