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.

A332421 The number of regions inside a nonagon 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

154, 2754, 16858, 55098, 142318, 298350, 568162, 975294, 1585666, 2426292, 3588508, 5093604, 7067422, 9523746, 12612214, 16351218, 20924029, 26326026, 32789107, 40289238, 49093282, 59181228, 70852528
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

Keywords

Comments

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

Links

Crossrefs

Cf. A332427 (n-gons), A332428 (vertices), A332429 (edges), A007678, A092867, A331452, A331929.

Extensions

a(6)-a(23) from Lars Blomberg, May 16 2020

A332427 Irregular table read by rows: Take a nonagon with all diagonals drawn, as in A332421. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

Original entry on oeis.org

90, 36, 18, 9, 0, 0, 1, 1332, 918, 414, 90, 6525, 6453, 2529, 1071, 171, 90, 10, 9, 22248, 18882, 10368, 2988, 486, 108, 18, 54558, 50985, 24750, 9387, 2034, 531, 36, 27, 9, 0, 0, 0, 0, 0, 0, 1, 113958, 107676, 54558, 17820, 3672, 612, 36, 18
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

Keywords

Comments

See the links in A332421 for images of the nonagons.

Examples

			A nonagon with no other points along its edges, n = 1, contains 90 triangles, 36 quadrilaterals, 18 pentagons, 9 hexagons, 1 nonagon and no other n-gons, so the first row is [90,36,18,9,0,0,1]. A nonagon with 1 point dividing its edges, n = 2, contains 1332 triangles, 918 quadrilaterals, 414 pentagons, 90 hexagons and no other n-gons, so the second row is [1332,918,414,90].
Table begins:
90,36,18,9,0,0,1;
1332,918,414,90;
6525,6453,2529,1071,171,90,10,9;
22248,18882,10368,2988,486,108,18;
54558,50985,24750,9387,2034,531,36,27,9,0,0,0,0,0,0,1;
113958,107676,54558,17820,3672,612,36,18;
210591,208089,105417,34407,7560,1737,307,45,0,9;
The row sums are A332421.

Links

Crossrefs

Cf. A332421 (regions), A332428 (vertices), A332429 (edges), A007678, A092867, A331452, A331929.

Extensions

a(36) and beyond from Lars Blomberg, May 16 2020

A332428 The number of vertices on a nonagon 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

135, 2395, 16434, 53155, 141147, 293374, 565767, 966493, 1580940, 2411533, 3581613, 5070655, 7057026, 9493435, 12594564, 16307974, 20902338, 26269597, 32760774, 40217905, 49049919, 59090671, 70803180
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

Keywords

Comments

See the links in A332421 for images of the nonagons.

Crossrefs

Cf. A332421 (regions), A332427 (n-gons), A332429 (edges), A330846, A092866, A332599, A007569.

Extensions

a(6)-a(23) from Lars Blomberg, May 16 2020

A335783 a(n) is the number of edges formed by n-secting the angles of a nonagon (enneagon).

Original entry on oeis.org

9, 36, 261, 279, 783, 846, 288, 1557, 2583, 2664, 3897, 3996, 5661, 2214, 7407, 7425, 9603, 9549, 11997, 12231, 9738, 14607, 17667, 17730, 20781, 20997, 24669, 16515, 27873, 28278, 32301, 32202, 36657, 36981, 32706, 40698, 46161, 46143, 51039, 51462, 56979
Offset: 1

Views

Author

Lars Blomberg, Jun 24 2020

Keywords

Comments

See A335781 for illustrations.

Links

Crossrefs

Cf. A332429 (n-sected sides, not angles), A335781 (regions), A335782 (vertices), A335784 (ngons).

A367324 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 edges in the resulting planar graph.

Original entry on oeis.org

3, 21, 8, 132, 92, 20, 429, 596, 290, 42, 1272, 1936, 2215, 708, 91, 2826, 6020, 7405, 4020, 1575, 136, 5640, 11088, 21150, 15120, 10962, 2632, 288, 10461, 26260, 43490, 38544, 35812, 17728, 5148, 390, 17094, 42144, 88230, 83136, 96257, 60672, 33291, 7800, 715
Offset: 3

Views

Author

Scott R. Shannon and N. J. A. Sloane, Nov 14 2023

Keywords

Comments

See A367322, A367323 and the cross references for images of the n-gons.

Examples

			The table begins:
3, 21, 132, 429, 1272, 2826, 5640, 10461, 17094, 26847, 41046, 61041, 84051, ...
8, 92, 596, 1936, 6020, 11088, 26260, 42144, 72296, 107832, 183340, 222940, ...
20, 290, 2215, 7405, 21150, 43490, 88230, 151135, 250825, 384360, 578840, ...
42, 708, 4020, 15120, 38544, 83136, 169686, 294678, 475500, 746340, 1140624, ...
91, 1575, 10962, 35812, 96257, 201054, 389991, 668458, 1096508, 1675835, ...
136, 2632, 17728, 60672, 163776, 341920, 673112, 1155144, 1892528, 2905088, ...
288, 5148, 33291, 108252, 283464, 591723, 1133928, 1941786, 3166605, 4837824, ...
390, 7800, 48870, 164470, 430840, 900890, 1735800, 2982660, 4849740, 7438490, ...
715, 12793, 79134, 255552, 660033, 1376870, 2619287, 4482654, 7284904, ...
756, 16512, 99348, 346140, 912960, 1894920, 3685056, 6313164, 10261200, ...
1508, 26806, 160641, 516932, 1322802, 2757339, 5221996, 8932664, 14483183, ...
1722, 35546, 210658, 696682, 1773828, 3718400, 7030464, 12067720, 19517596, ...
2835, 49995, 292590, 939720, 2388825, 4976130, 9394815, 16064970, 26003640, ...
3088, 63456, 370784, 1217664, 3081472, 6455872, 12162640, 20861328, 33700320, ...
4896, 85680, 493017, 1579436, 3995102, 8318525, 15667336, 26783636, ...
4320, 99036, 593784, 1958922, 4978872, 10395450, 19644408, ...
7923, 137693, 781470, 2499792, 6298633, 13109658, 24645983, ...
8360, 167160, 941940, 3068280, 7705420, 16112480, 30238400, ...
12180, 210378, 1180683, 3772692, 9476418, 19717089, ...
12782, 252296, 1400674, 4547884, 11375584, 23776236, ...
17963, 308591, 1716306, 5478232, 13725457, 28550084, ...
16344, 350448, 1981416, 6460080, 16185624, ...
25600, 437700, 2415825, 7704700, 19262750, ...
.
.
.

Crossrefs

Cf. A367322 (vertices), A367323 (regions), A274586 (1st row), A331448 (2nd row), A329710 (3rd row), A330845 (4th row), A333112 (5th row), A333110 (6th row), A332429 (7th row), A332419 (8th row), A135565 (1st column).

Formula

T(n,k) = A367322(n,k) + A367323(n,k) - 1 (Euler).
Showing 1-5 of 5 results.

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

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