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
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
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
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;
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
- Lars Blomberg, Table of n, a(n) for n = 1..80
- 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.
Showing 1-4 of 4 results.
Comments