cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A330911 The number of edges formed by straight line segments mutually connecting all vertices of a semicircular polygon defined in A333642.

Original entry on oeis.org

5, 15, 35, 76, 142, 251, 408, 576, 947, 1367, 1845, 2600, 3460, 4011, 5822, 7386, 9023, 11423, 13967, 16242, 20330, 24235, 28222, 33686, 39327, 44967, 52733, 60608, 67383, 78947, 89530, 100040, 113885, 127791, 141925, 159356, 177158, 194895, 217232, 239662
Offset: 1

Views

Author

Keywords

Comments

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

Crossrefs

Cf. A333642 (regions), A330913 (vertices), A330914 (n-gons), A333278, A333027, A135565.

Extensions

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

Views

Author

Keywords

Comments

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

Crossrefs

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

Extensions

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

Views

Author

Keywords

Comments

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

Examples

			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;
		

Crossrefs

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

A333643 Number of regions in a polygon whose boundary consists of n+2 equally spaced points around the arc of a semicircle. See Comments for precise definition.

Original entry on oeis.org

1, 4, 11, 25, 50, 91, 154, 234, 375, 550, 769, 1079, 1456, 1783, 2500, 3196, 3987, 5016, 6175, 7348, 9086, 10879, 12836, 15250, 17875, 20682, 24129, 27811, 31419, 36425, 41416, 46664, 52921, 59500, 66489, 74481, 82954, 91807, 102050, 112750, 123700, 136654
Offset: 1

Views

Author

Keywords

Comments

A semicircular polygon with n+2 points is created by placing n+2 equally spaced vertices along a semicircle's arc, which includes the 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.
Note that there is a curious relationship between the terms of this sequence and the number of regions in the 'general position' polygon given in A006522. They are a match except for every third term starting at a(8) = 234. Examining the images for n = 8,11,14,17 shows that these polygons have interior points at which three or more lines intersect, while the other n values have no such intersection points. Such multi-line intersection points will reduce the number of regions as compared to the general position polygon which has no multi-line intersection points. This is reflected by the terms in this sequence being lower than the corresponding value in A006522 for n = 8,11,14,... . Why every third value of n in this sequence starting at n = 8 leads to polygons having multiple line intersection points while other values of n do not is currently not known.

Crossrefs

Extensions

More terms from Lars Blomberg, Apr 20 2020
Showing 1-4 of 4 results.