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

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Author

Keywords

Comments

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

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

Keywords

Comments

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

Crossrefs

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

A340614 Irregular table read by rows: Take a Reuleaux triangle with all diagonals drawn, as in A340639. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

Original entry on oeis.org

1, 18, 6, 79, 51, 12, 3, 252, 192, 60, 6, 6, 576, 600, 168, 73, 15, 1170, 1380, 390, 126, 6, 12, 2248, 2589, 894, 288, 66, 18, 3, 4026, 4332, 1662, 480, 108, 30, 6426, 7182, 2988, 943, 189, 36, 9942, 11268, 4470, 1266, 300, 84, 0, 6, 14508, 16941, 7098, 2119, 435, 120, 6, 6
Offset: 1

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Author

Keywords

Comments

See A340639 for images of the regions and A340644 for images of the vertices.

Examples

			A Reuleaux triangle with 1 point dividing its edges, n = 2, contains 18 triangles, 6 quadrilaterals and no other n-gons, so the second row is [18, 6]. A Reuleaux triangle with 2 points dividing its edges, n = 3, contains 79 triangles, 51 quadrilaterals, 12 pentagons, 3 hexagons and no other n-gons, so the third row is [79, 51, 12, 3].
The table begins:
1;
18, 6;
79, 51, 12, 3;
252, 192, 60, 6, 6;
576, 600, 168, 73, 15;
1170, 1380, 390, 126, 6, 12;
2248, 2589, 894, 288, 66, 18, 3;
4026, 4332, 1662, 480, 108, 30;
6426, 7182, 2988, 943, 189, 36;
9942, 11268, 4470, 1266, 300, 84, 0, 6;
14508, 16941, 7098, 2119, 435, 120, 6, 6;
21234, 23598, 10194, 3090, 636, 132, 12, 6;
28881, 34086, 13935, 4528, 1041, 177, 24, 3;
39588, 45384, 19470, 5796, 1380, 198, 48;
52197, 60744, 26409, 7831, 1914, 366, 21, 15;
68646, 78492, 33810, 10668, 2358, 396, 60;
87642, 100701, 44670, 13942, 2931, 555, 66, 21, 6;
111084, 127290, 55818, 17082, 3912, 696, 132, 6;
138453, 158907, 70158, 22233, 4869, 1002, 87, 15, 0, 4;
171276, 194622, 87312, 26748, 6132, 846, 174, 6, 6;
		

Crossrefs

Cf. A340639 (regions), A340644 (vertices), A340613 (edges), A007678, A092867.

A340687 The number of edges on a concave circular 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, 21, 51, 177, 354, 852, 1686, 3036, 5994, 8550, 12933, 16938, 24303, 30192, 41616, 52581, 66600, 82857, 101199, 128409, 153669, 194505, 227193, 271635, 320898, 368703, 431640, 490884, 578805, 646869, 744717, 851214, 943068, 1071741, 1195638, 1367913, 1523694, 1713300, 1885389, 2082696
Offset: 1

Views

Author

Keywords

Comments

The terms are from numeric computation - no formula for a(n) is currently known.
See A340685 for images of the regions and A340686 for images of the vertices.

Crossrefs

Cf. A340685 (regions), A340686 (vertices), A340688 (n-gons), A340613, A007678, A092867.

A342152 The number of edges on a vesica piscis 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

2, 8, 42, 148, 438, 936, 2010, 3462, 6038, 8816, 14606, 20504, 29854, 39790, 54618, 70142, 92662, 115718, 147494, 177500, 223506, 267872, 326142, 384274, 460302, 535896, 631886, 726674, 848126, 965592, 1115194, 1259926, 1440558, 1616940, 1833130, 2042602, 2300498, 2549756, 2851626, 3139854
Offset: 1

Views

Author

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.

Crossrefs

Cf. A341877 (regions), A341878 (vertices), A342153 (n-gons), A135565, A332376, A340613, A340687.

Formula

a(n) = A341877(n) + A341878(n) - 1.
Showing 1-5 of 5 results.