cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

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Author

Keywords

Comments

The terms are from numeric computation - no formula for a(n) is currently known.

Crossrefs

Cf. A331932 (n-gons), A330845 (edges), A330846 (vertices), A007678, A092867, A331452, A331929.

Extensions

a(9)-a(30) from Lars Blomberg, May 12 2020

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

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Author

Keywords

Comments

See the links in A331931 for images of the hexagons.

Crossrefs

Cf. A331931 (regions), A331932 (n-gons), A330846 (vertices), A274586 , A332600, A331765.

Extensions

a(9)-a(30) from Lars Blomberg, May 12 2020

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

Views

Author

Keywords

Comments

See the links in A331931 for images of the hexagons.

Crossrefs

Cf. A331931 (regions), A331932 (n-gons), A330845 (edges), A092866, A332599, A007569.

Extensions

a(9)-a(30) from Lars Blomberg, May 12 2020

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

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Author

Keywords

Comments

See A333642 for a precise definition of the polygon and images.

Examples

			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;
		

Crossrefs

Cf. A333642 (regions), A330911 (edges), A330913 (vertices), A331932, A333025, A331451.

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

Views

Author

Lars Blomberg, Jun 21 2020

Keywords

Comments

For n<=200 no polygon has more than 12 edges.

Examples

			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;
		

Crossrefs

Cf. A331932 (n-sected sides, not angles), A335733 (regions), A335734 (vertices), A335735 (edges).
Showing 1-5 of 5 results.