A331931
The number of regions inside a hexagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
Original entry on oeis.org
24, 408, 2268, 8208, 20832, 44640, 89214, 154752, 249906, 390012, 590658, 824712, 1183704, 1580868, 2067162, 2770476, 3585582, 4397172, 5665818, 6827736, 8318976, 10209948, 12364098, 14395164, 17194230, 20216808, 23436612, 27124416, 31817676, 35516328
Offset: 1
- Scott R. Shannon, Hexagon regions for n = 1.
- Scott R. Shannon, Hexagon regions for n = 2.
- Scott R. Shannon, Hexagon regions for n = 3.
- Scott R. Shannon, Hexagon regions for n = 4.
- Scott R. Shannon, Hexagon regions for n = 5.
- Scott R. Shannon, Hexagon regions for n = 6.
- Scott R. Shannon, Hexagon regions for n = 7.
- Scott R. Shannon, Hexagon regions for n = 8.
- Scott R. Shannon, Hexagon regions for n = 5, with random distance-based coloring.
- Scott R. Shannon, Hexagon regions for n = 6, with random distance-based coloring.
- Wikipedia, Hexagon.
A330845
The number of edges inside a hexagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
Original entry on oeis.org
42, 708, 4020, 15120, 38544, 83136, 169686, 294678, 475500, 746340, 1140624, 1581612, 2296986, 3055734, 3980526, 5391264, 7003662, 8516346, 11094810, 13280970, 16180932, 19971282, 24277212, 28090218, 33683862, 39656604, 45901494, 53121744, 62678268, 69382632
Offset: 1
A330846
The number of vertices inside a hexagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
Original entry on oeis.org
19, 301, 1753, 6913, 17713, 38497, 80473, 139927, 225595, 356329, 549967, 756901, 1113283, 1474867, 1913365, 2620789, 3418081, 4119175, 5428993, 6453235, 7861957, 9761335, 11913115, 13695055, 16489633, 19439797, 22464883, 25997329, 30860593, 33866305
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;
A335736
Irregular table read by rows: n-sect the angles of a hexagon. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.
Original entry on oeis.org
0, 0, 0, 1, 6, 24, 30, 6, 0, 0, 0, 0, 0, 0, 1, 18, 6, 84, 54, 30, 12, 0, 0, 0, 0, 0, 1, 114, 36, 24, 168, 120, 60, 24, 6, 0, 0, 0, 0, 1, 132, 78, 18, 6, 252, 264, 60, 48, 6, 6, 0, 0, 0, 1, 276, 240, 78, 12, 408, 324, 150, 84, 0, 6, 0, 0, 0, 1, 366, 216, 96, 30
Offset: 1
The table begins
0, 0, 0, 1;
6;
24, 30, 6, 0, 0, 0, 0, 0, 0, 1;
18, 6;
84, 54, 30, 12, 0, 0, 0, 0, 0, 1;
114, 36, 24;
168, 120, 60, 24, 6, 0, 0, 0, 0, 1;
132, 78, 18, 6;
252, 264, 60, 48, 6, 6, 0, 0, 0, 1;
276, 240, 78, 12;
408, 324, 150, 84, 0, 6, 0, 0, 0, 1;
366, 216, 96, 30;
Showing 1-5 of 5 results.
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