A332953
The number of regions formed inside an isosceles triangle by straight line segments mutually connecting all vertices and all points that divide the two equal length sides into n equal parts; the base of the triangle contains no points other than its vertices.
Original entry on oeis.org
1, 5, 18, 52, 125, 257, 486, 832, 1333, 2027, 3048, 4304, 6057, 8167, 10749, 13929, 18058, 22664, 28533, 34981, 42519, 51425, 62118, 73473, 86768, 101902, 118695, 137138, 159147, 181752, 208813, 237209, 268614, 303718, 340882, 380811, 427540, 477134, 530047
Offset: 1
- Lars Blomberg, Table of n, a(n) for n = 1..70
- 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 = 6.
- Scott R. Shannon, Illustration for n = 8.
- 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 = 5 with random distance-based coloring.
- Scott R. Shannon, Illustration for n = 10 with random distance-based coloring.
- Scott R. Shannon, Illustration for n = 15 with random distance-based coloring.
A333025
Irregular table read by rows: Take an isosceles triangle with its equal length sides divided into n equal parts with all diagonals drawn, as in A332953. Then T(n,k) = number of k-sided polygons in that figure for k>=3.
Original entry on oeis.org
1, 5, 14, 3, 1, 29, 19, 4, 50, 66, 9, 81, 164, 12, 134, 313, 37, 2, 219, 546, 60, 7, 359, 853, 112, 9, 556, 1294, 160, 16, 1, 779, 1940, 283, 43, 3, 1105, 2780, 360, 53, 6, 1540, 3750, 670, 91, 5, 1, 2087, 5064, 873, 132, 11, 2806, 6625, 1144, 164, 7, 3
Offset: 1
Table begins:
1;
5;
14, 3, 1;
29, 19, 4;
50, 66, 9;
81, 164, 12;
134, 313, 37, 2;
219, 546, 60, 7;
359, 853, 112, 9;
556, 1294, 160, 16, 1;
779, 1940, 283, 43, 3;
1105, 2780, 360, 53, 6;
1540, 3750, 670, 91, 5, 1;
2087, 5064, 873, 132, 11;
2806, 6625, 1144, 164, 7, 3;
The row sums are A332953.
A333027
The number of edges formed on an isosceles triangle by straight line segments mutually connecting all vertices and all points that divide the two equal length sides into n equal parts; the base of the triangle contains no points other than its vertices.
Original entry on oeis.org
3, 10, 33, 96, 235, 486, 933, 1600, 2561, 3884, 5907, 8310, 11793, 15890, 20863, 27002, 35229, 44117, 55820, 68312, 82931, 100368, 121711, 143685, 169750, 199509, 232366, 268169, 312132, 355839, 409902, 465503, 527080, 596443, 668961, 746443, 839830, 937967
Offset: 1
A357007
Number of vertices in an equilateral triangle when n internal equilateral triangles are drawn between the 3n points that divide each side into n+1 equal parts.
Original entry on oeis.org
3, 6, 15, 30, 51, 66, 111, 150, 171, 246, 303, 312, 435, 510, 543, 678, 771, 765, 975, 1059, 1131, 1326, 1455, 1488, 1731, 1878, 1899, 2178, 2355, 2376, 2703, 2886, 2955, 3270, 3444, 3420, 3891, 4110, 4191, 4485, 4803, 4878, 5295, 5526, 5544, 6078, 6351, 6396, 6915, 7206, 7311, 7794, 8115
Offset: 0
- Scott R. Shannon, Table of n, a(n) for n = 0..250
- Scott R. Shannon, Image for n = 1.
- Scott R. Shannon, Image for n = 2.
- Scott R. Shannon, Image for n = 3.
- Scott R. Shannon, Image for n = 5. This is the first term that forms intersections with non-simple vertices.
- Scott R. Shannon, Image for n = 10.
- Scott R. Shannon, Image for n = 50.
- Scott R. Shannon, Image for n = 100.
- Scott R. Shannon, Image for n = 200.
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
Showing 1-5 of 5 results.
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