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
A330847
The number of vertices inside a pentagon 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
10, 121, 1055, 3506, 10410, 21111, 43740, 74526, 124490, 190291, 288190, 403321, 573805, 771191, 1027550, 1331896, 1721765, 2157301, 2712175, 3322441, 4067325, 4904491, 5900185, 6975151, 8268755, 9678566, 11297345, 13060231, 15102955, 17263311, 19784995
Offset: 1
A331932
Triangle read by rows: Take a hexagon with all diagonals drawn, as in A331931. Then T(n,k) = number of k-sided polygons in that figure for k = 3, 4, ..., n+4.
Original entry on oeis.org
18, 6, 0, 264, 108, 36, 0, 1344, 654, 252, 12, 6, 4164, 2772, 1020, 228, 24, 0, 10038, 7758, 2424, 516, 72, 24, 0, 21108, 16188, 6060, 1128, 156, 0, 0, 0, 39690, 32022, 13368, 3654, 432, 48, 0, 0, 0, 68052, 56616, 22980, 6084, 888, 120, 12, 0, 0, 0
Offset: 1
A hexagon with no other points along its edges, n = 1, contains 18 triangles, 6 quadrilaterals and no other n-gons, so the first row is [18,6,0]. A hexagon with 1 point dividing its edges, n = 2, contains 264 triangles, 108 quadrilaterals, 36 pentagons and no other n-gons, so the second row is [264,108,36,0].
Triangle begins:
18,6,0
264,108,36,0
1344,654,252,12,6
4164,2772,1020,228,24,0
10038,7758,2424,516,72,24,0
21108,16188,6060,1128,156,0,0,0
39690,32022,13368,3654,432,48,0,0,0
68052,56616,22980,6084,888,120,12,0,0,0
The row sums are A331931.
A332418
The number of vertices on a decagon 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
171, 3581, 23651, 80191, 213041, 444251, 862711, 1481141, 2413721, 3701951, 5493891, 7765621, 10833601, 14589491, 19315751, 25064491, 32107771, 40337021, 50328771, 61790891, 75318371
Offset: 1
A332428
The number of vertices on a nonagon 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
135, 2395, 16434, 53155, 141147, 293374, 565767, 966493, 1580940, 2411533, 3581613, 5070655, 7057026, 9493435, 12594564, 16307974, 20902338, 26269597, 32760774, 40217905, 49049919, 59090671, 70803180
Offset: 1
A333109
The number of vertices on an octagon 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
57, 1145, 8417, 29121, 80345, 167105, 333297, 570969, 939113, 1441153, 2153937, 3029913, 4262929, 5741473, 7606745, 9876585, 12690553, 15921777, 19922289, 24430633, 29834073, 35990065, 43151521, 51068689
Offset: 1
A333113
The number of vertices inside a heptagon 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, 5369, 17417, 47796, 99261, 194278, 331955, 546805, 833946, 1245314, 1762265, 2461837, 3311680, 4402405, 5700598, 7322231, 9200878, 11494161, 14108123, 17224438, 20752264, 24894009, 29506128, 34854099, 40780391, 47552050
Offset: 1
A357197
Number of vertices in a hexagon when n internal hexagons are drawn between the 6n points that divide each side into n+1 equal parts.
Original entry on oeis.org
6, 12, 30, 60, 102, 156, 222, 300, 390, 468, 606, 708, 870, 1020, 1152, 1356, 1542, 1740, 1950, 2112, 2406, 2652, 2910, 3072, 3462, 3756, 4062, 4350, 4710, 4974, 5406, 5772, 6126, 6540, 6918, 7260, 7782, 8220, 8646, 8946, 9606, 10032, 10590, 11052, 11568, 12156, 12702, 13116, 13830, 14388
Offset: 0
A335734
a(n) is the number of vertices formed by n-secting the angles of a hexagon.
Original entry on oeis.org
6, 7, 66, 19, 186, 145, 384, 199, 642, 547, 978, 631, 1332, 1231, 1824, 1351, 2298, 2191, 2952, 2281, 3546, 3415, 4356, 3583, 5070, 4849, 6036, 5101, 6858, 6583, 7968, 6901, 8928, 8611, 10152, 8965, 11250, 10897, 12606, 11257, 13824, 13459, 15336, 13903, 16692
Offset: 1
Showing 1-10 of 11 results.
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