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 1-4 of 4 results.

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

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Author

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;
		

Crossrefs

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

A340686 The number of vertices 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, 10, 24, 76, 168, 391, 819, 1447, 2949, 4153, 6393, 8293, 12048, 14857, 20670, 25972, 33123, 41026, 50379, 63700, 76560, 96628, 113262, 135076, 160050, 183484, 215355, 244435, 288861, 322276, 371742, 424279, 470838, 534376, 597033, 682264, 760959, 854755, 941706, 1039255, 1141569, 1254190
Offset: 1

Views

Author

Keywords

Comments

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

Crossrefs

Cf. A340685 (regions), A340687 (edges), A340688 (n-gons), A340644, 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.

A341877 The number of regions inside 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

1, 4, 24, 84, 236, 508, 1048, 1820, 3110, 4644, 7428, 10520, 15108, 20288, 27576, 35632, 46652, 58548, 74156, 89992, 112288, 135064, 163684, 193572, 230884, 269612, 316846, 365496, 425060, 485392, 558744, 632888, 721636, 811724, 918040, 1025224, 1151904, 1279188, 1427720, 1575496
Offset: 1

Views

Author

Keywords

Comments

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

Crossrefs

Cf. A341878 (vertices), A342152 (edges), A342153 (n-gons), A007678, A092867, A340639, A340685.
Showing 1-4 of 4 results.