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.

A340639 The number of regions inside a Reuleaux triangle 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

1, 24, 145, 516, 1432, 3084, 6106, 10638, 17764, 27336, 41233, 58902, 82675, 111864, 149497, 194430, 250534, 316020, 395728, 487122, 596434, 720162, 865321, 1027974, 1216291, 1425348, 1664539, 1928022, 2226658, 2553204, 2920378, 3319536, 3764848, 4246638, 4780489, 5355414, 5988973
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Jan 14 2021

Keywords

Comments

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

Links

Crossrefs

Cf. A340644 (vertices), A340613 (edges), A340614 (n-gons), A007678, A092867.

A340644 The number of vertices on a Reuleaux triangle 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

3, 19, 120, 442, 1332, 2863, 5871, 10171, 17358, 26518, 40590, 57757, 81735, 110209, 148158, 192184, 248772, 313105, 393429, 483283, 593490, 715528, 861660, 1022281, 1211811, 1418515, 1659108, 1919842, 2220204, 2543527, 2912751, 3308305, 3755922, 4233730, 4770150, 5340529, 5977071
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Jan 14 2021

Keywords

Comments

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

Links

Crossrefs

Cf. A340639 (regions), A340613 (edges), A340614 (n-gons), A007678, A092867.

A340613 The number of edges on a Reuleaux triangle 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

3, 42, 264, 957, 2763, 5946, 11976, 20808, 35121, 53853, 81822, 116658, 164409, 222072, 297654, 386613, 499305, 629124, 789156, 970404, 1189923, 1435689, 1726980, 2050254, 2428101, 2843862, 3323646, 3847863, 4446861, 5096730, 5833128, 6627840, 7520769, 8480367, 9550638, 10695942, 11966043
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Jan 14 2021

Keywords

Comments

The terms are from numeric computation - no formula for a(n) is currently known.
See A340639 for images of the regions and A340644 for images of the vertices.

Links

Crossrefs

Cf. A340639 (regions), A340644 (vertices), A340614 (n-gons), A007678, A092867.

A340688 Irregular table read by rows: Take a concave circular triangle with all diagonals drawn, as in A340685. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

Original entry on oeis.org

1, 12, 22, 3, 3, 66, 36, 67, 108, 12, 222, 186, 48, 6, 265, 465, 132, 6, 582, 786, 174, 48, 732, 1905, 324, 76, 3, 6, 1410, 2268, 558, 156, 6, 1704, 3732, 861, 223, 18, 3, 2778, 4242, 1260, 324, 42, 3369, 6540, 1872, 409, 42, 24, 4896, 7302, 2502, 540, 72, 24, 6138, 10467, 3306, 907, 99, 30
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Jan 16 2021

Keywords

Comments

See A340685 for images of the regions and A340686 for images of the vertices.

Examples

			A concave circular triangle with 1 point dividing its edges, n = 2, contains 12 triangles and no other n-gons, so the second row is [12]. A concave circular triangle with 2 points dividing its edges, n = 3, contains 22 triangles, 3 quadrilaterals, 3 pentagons and no other n-gons, so the third row is [22, 3, 3].
The table begins:
1;
12;
22, 3, 3;
66, 36;
67, 108, 12;
222, 186, 48, 6;
265, 465, 132, 6;
582, 786, 174, 48;
732, 1905, 324, 76, 3, 6;
1410, 2268, 558, 156, 6;
1704, 3732, 861, 223, 18, 3;
2778, 4242, 1260, 324, 42;
3369, 6540, 1872, 409, 42, 24;
4896, 7302, 2502, 540, 72, 24;
6138, 10467, 3306, 907, 99, 30;
8364, 12522, 4566, 1020, 120, 18;
10132, 16149, 5439, 1410, 288, 57, 0, 3;
13398, 19308, 6870, 1962, 252, 30, 12;
16029, 23082, 8859, 2422, 336, 90, 3;
20682, 29658, 10800, 2976, 528, 66;

Links

Crossrefs

Cf. A340685 (regions), A340686 (vertices), A340687 (edges), A340614, A007678, A092867.

A342153 Irregular table read by rows: Take a vesica piscis with all diagonals drawn, as in A341877. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

Original entry on oeis.org

0, 4, 18, 6, 52, 28, 4, 120, 78, 34, 4, 252, 188, 56, 12, 470, 348, 184, 40, 4, 2, 808, 648, 300, 56, 8, 1282, 1118, 548, 138, 20, 4, 2036, 1772, 644, 156, 28, 8, 2878, 2804, 1252, 388, 96, 10, 4172, 4024, 1728, 468, 100, 28, 5752, 5682, 2600, 866, 162, 46, 7912, 7676, 3420, 1024, 196, 44, 16
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 02 2021

Keywords

Comments

The terms are from numeric computation - no formula for a(n) is currently known.
See A341877 for images of the regions and A341878 for images of the vertices.

Examples

			A vesica piscis with 1 point dividing its edges, n = 2, contains 4 triangles and no other n-gons, so the second row is [4]. A vesica piscis with 3 points dividing its edges, n = 4, contains 52 triangles, 28 quadrilaterals, 4 pentagons and no other n-gons, so the fourth row is [52, 28, 4].
The table begins:
0;
4;
18,6;
52,28,4;
120,78,34,4;
252,188,56,12;
470,348,184,40,4,2;
808,648,300,56,8;
1282,1118,548,138,20,4;
2036,1772,644,156,28,8;
2878,2804,1252,388,96,10;
4172,4024,1728,468,100,28;
5752,5682,2600,866,162,46;
7912,7676,3420,1024,196,44,16;
10388,10354,4868,1548,352,60,6;
13496,13808,6016,1836,388,80,4,0,4;
17310,17590,8376,2672,564,122,16,2;
22012,22364,10160,3152,712,124,20,4;
27440,27956,13162,4432,964,172,24,2,4;
33784,34736,15588,4640,1096,120,28;

Links

Crossrefs

Cf. A341877 (regions), A342152 (edges), A341878 (vertices), A331451, A331911, A340614, A340688.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.