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 1-3 of 3 results.

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

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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.

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;
		

Crossrefs

Cf. A341877 (regions), A342152 (edges), A341878 (vertices), A331451, A331911, A340614, A340688.

A341878 The number of vertices 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, 5, 19, 65, 203, 429, 963, 1643, 2929, 4173, 7179, 9985, 14747, 19503, 27043, 34511, 46011, 57171, 73339, 87509, 111219, 132809, 162459, 190703, 229419, 266285, 315041, 361179, 423067, 480201, 556451, 627039, 718923, 805217, 915091, 1017379, 1148595, 1270569, 1423907, 1564359
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. A341877 (regions), A342152 (edges), A342153 (n-gons), A007569, A092866, A340644, A340686.

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 1-3 of 3 results.