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.

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

Views

Author

Keywords

Comments

See the links in A333139 for images of the decagons.

Crossrefs

Cf. A333139 (regions), A332417 (n-gons), A332418 (vertices), A330845, A274586, A332600, A331765.

Extensions

a(6)-a(21) from Lars Blomberg, May 18 2020

A333139 The number of regions inside 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

220, 4220, 25220, 84280, 217800, 456640, 873090, 1501520, 2436020, 3736540, 5523970, 7830800, 10879460, 14665340, 19398660, 25173960, 32203320, 40502280, 50458120, 61995140, 75517160
Offset: 1

Views

Author

Keywords

Comments

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

Crossrefs

Cf. A332417 (n-gons), A332418 (vertices), A332419 (edges), A007678, A092867, A331452, A331929.

Extensions

a(6)-a(21) from Lars Blomberg, May 18 2020

A332417 Irregular table read by rows: Take a decagon with all diagonals drawn, as in A333139. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

Original entry on oeis.org

120, 90, 10, 2040, 1580, 460, 140, 10860, 8570, 4170, 1380, 210, 20, 10, 34360, 30420, 14240, 4020, 1120, 100, 20, 85600, 76920, 38610, 13360, 2650, 550, 110, 176760, 166400, 82560, 24500, 5500, 760, 140, 20, 327550, 320520, 159860, 51610, 10960, 2250, 300, 30, 0, 10
Offset: 1

Views

Author

Keywords

Comments

See the links in A333139 for images of the decagons.

Examples

			A decagon with no other points along its edges, n = 1, contains 120 triangles, 90 quadrilaterals, 10 pentagons and no other n-gons, so the first row is [120, 90, 10]. A decagon with 1 point dividing its edges, n = 2, contains 2040 triangles, 1580 quadrilaterals, 460 pentagons, 140 hexagons and no other n-gons, so the second row is [2040,1580,460,140].
Table begins:
120, 90, 10;
2040,1580,460,140;
10860,8570,4170,1380,210,20,10;
34360,30420,14240,4020,1120,100,20;
85600,76920,38610,13360,2650,550,110;
176760, 166400, 82560, 24500, 5500, 760, 140, 20;
327550, 320520, 159860, 51610, 10960, 2250, 300, 30, 0, 10;
565060, 549520, 277360, 86540, 18960, 3560, 480, 20, 20;
910920, 891290, 447790, 147300, 32180, 5640, 720, 130, 40, 10;
The row sums are A333139.
		

Crossrefs

Cf. A333139 (regions), A332418 (vertices), A332419 (edges), A007678, A092867, A331452, A331929.

Extensions

a(29) and beyond from Lars Blomberg, May 18 2020

A335801 a(n) is the number of vertices formed by n-secting the angles of a decagon.

Original entry on oeis.org

10, 11, 160, 31, 480, 371, 990, 171, 1570, 1431, 2380, 1551, 3370, 3131, 4600, 2211, 5790, 5481, 7230, 5851, 8910, 8521, 10830, 5751, 12600, 12151, 14730, 12721, 17110, 16541, 19730, 14231, 21950, 21531, 24910, 22201, 27920, 27201, 31220, 24181, 33810, 33501
Offset: 1

Views

Author

Lars Blomberg, Jun 25 2020

Keywords

Crossrefs

Cf. A332418 (n-sected sides, not angles), A335800 (regions), A335802 (edges), A335803 (ngons).

A367322 Table read by antidiagonals: Place k equally spaced points on each side of a regular n-gon and join every pair of the n*(k+1) boundary points by a chord; T(n,k) (n >= 3, k >= 0) gives the number of vertices in the resulting planar graph.

Original entry on oeis.org

3, 10, 5, 58, 37, 10, 178, 257, 121, 19, 558, 817, 1055, 301, 42, 1255, 2757, 3506, 1753, 708, 57, 2532, 4825, 10410, 6913, 5369, 1145, 135, 4786, 12293, 21111, 17713, 17417, 8417, 2395, 171, 7804, 19241, 43740, 38497, 47796, 29121, 16434, 3581, 341
Offset: 3

Views

Author

Keywords

Comments

See A367323 and the cross references for further images of the n-gons.

Examples

			The table begins:
3, 10, 58, 178, 558, 1255, 2532, 4786, 7804, 12292, 18966, 28540, 39117, 56107, ...
5, 37, 257, 817, 2757, 4825, 12293, 19241, 33549, 49577, 87685, 101981, 178465, ...
10, 121, 1055, 3506, 10410, 21111, 43740, 74526, 124490, 190291, 288190, ...
19, 301, 1753, 6913, 17713, 38497, 80473, 139927, 225595, 356329, 549967, ...
42, 708, 5369, 17417, 47796, 99261, 194278, 331955, 546805, 833946, 1245314, ...
57, 1145, 8417, 29121, 80345, 167105, 333297, 570969, 939113, 1441153, 2153937, ...
135, 2395, 16434, 53155, 141147, 293374, 565767, 966493, 1580940, 2411533, ...
171, 3581, 23651, 80191, 213041, 444251, 862711, 1481141, 2413721, 3701951, ...
341, 6062, 39248, 126061, 329131, 684223, 1307845, 2233815, 3639020, 5549952, ...
313, 7513, 47293, 167941, 450457, 931345, 1830625, 3132349, 5103589, 7825201, ...
728, 12845, 79859, 255711, 660140, 1372008, 2608476, 4454477, 7236853, ...
771, 16871, 103517, 343855, 881959, 1847525, 3504971, 6013953, 9739227, ...
1380, 24136, 145635, 465721, 1192710, 2478121, 4694040, 8014891, 12995535, ...
1393, 30305, 182785, 602337, 1533681, 3211873, 6067041, 10402769, 16824161, ...
2397, 41583, 245684, 783803, 1995341, 4145230, 7829333, 13366897, ...
1855, 46801, 291637, 967123, 2476873, 5166055, 9798175, ...
3895, 67090, 389690, 1241765, 3146533, 6535659, 12317567, ...
3861, 80921, 466141, 1522001, 3840181, 8027441, 15094521, ...
6006, 102817, 589029, 1875511, 4734786, 9833104, ...
5963, 122849, 694387, 2259005, 5671887, 11852105, ...
8878, 151180, 856589, 2725041, 6858600, 14242153, ...
7321, 169297, 979777, 3205921, 8068321, ...
12675, 214851, 1206050, 3834451, 9626475, ...
.
.
.
		

Crossrefs

Cf. A367323 (regions), A367324 (edges), A274585 (1st row), A331449 (2nd row), A330847 (3rd row), A330846 (4th row), A333113 (5th row), A333109 (6th row), A332428 (7th row), A332418 (8th row), A007569 (1st column).

Formula

T(n,k) = A367324(n,k) - A367323(n,k) + 1 (Euler).
Showing 1-5 of 5 results.