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.
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
A329710
The number of edges 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
20, 290, 2215, 7405, 21150, 43490, 88230, 151135, 250825, 384360, 578840, 814180, 1151525, 1550530, 2063225, 2676925, 3452460, 4333340, 5436210, 6668320, 8154980, 9837690, 11822175, 13993360, 16569650, 19401865, 22636495, 26182350, 30253225, 34608450, 39628050
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.
A332419
The number of edges 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
390, 7800, 48870, 164470, 430840, 900890, 1735800, 2982660, 4849740, 7438490, 11017860, 15596420, 21713060, 29254830, 38714410, 50238450, 64311090, 80839300, 100786890, 123786030, 150835530
Offset: 1
A332429
The number of edges 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
288, 5148, 33291, 108252, 283464, 591723, 1133928, 1941786, 3166605, 4837824, 7170120, 10164258, 14124447, 19017180, 25206777, 32659191, 41826366, 52595622, 65549880, 80507142, 98143200, 118271898, 141655707
Offset: 1
A333110
The number of edges 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
136, 2632, 17728, 60672, 163776, 341920, 673112, 1155144, 1892528, 2905088, 4327912, 6104696, 8557008, 11532288, 15271624, 19829528, 25447640, 31957872, 39935984, 49008392, 59807600, 72151536, 86465832, 102403360
Offset: 1
A333112
The number of edges 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
91, 1575, 10962, 35812, 96257, 201054, 389991, 668458, 1096508, 1675835, 2494989, 3536876, 4930408, 6639913, 8816458, 11425631, 14659085, 18433975, 23007579, 28257418, 34478871, 41557817, 49822388, 59079475, 69756253, 81641812, 95165210
Offset: 1
A335735
a(n) is the number of edges formed by n-secting the angles of a hexagon.
Original entry on oeis.org
6, 12, 126, 42, 366, 318, 762, 432, 1278, 1152, 1950, 1338, 2658, 2550, 3642, 2808, 4590, 4500, 5898, 4734, 7086, 6978, 8706, 7344, 10134, 9876, 12066, 10422, 13710, 13374, 15930, 14052, 17850, 17460, 20298, 18222, 22494, 22062, 25206, 22860, 27642, 27216
Offset: 1
A357198
Number of edges 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, 18, 54, 114, 198, 306, 438, 594, 774, 942, 1206, 1422, 1734, 2034, 2310, 2706, 3078, 3474, 3894, 4242, 4806, 5298, 5814, 6186, 6918, 7506, 8118, 8706, 9414, 9978, 10806, 11538, 12258, 13074, 13842, 14562, 15558, 16434, 17298, 17970, 19206, 20082, 21174, 22122, 23154, 24306, 25398, 26286
Offset: 0
Showing 1-10 of 11 results.
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