A007678 -id:A007678 - cp's OEIS frontend

A101363 In the interior of a regular 2n-gon with all diagonals drawn, the number of points where exactly three diagonals intersect.

0, 1, 8, 20, 60, 112, 208, 216, 480, 660, 864, 1196, 1568, 2250, 2464, 2992, 3924, 4332, 5160, 8148, 7040, 8096, 10560, 10600, 12064, 15552, 15288, 17052, 25320, 21080, 23360, 30360, 28288, 30940, 36288, 36852, 40128, 50076, 47120, 50840, 67620

Offset: 2

Graeme McRae, Dec 26 2004, revised Feb 23 2008, Feb 26 2008

nonn

When n is odd, there are no intersections in the interior of an n-gon where more than 2 diagonals meet.
When n is not a multiple of 6, there are no intersections in the interior of an n-gon where more than 3 diagonals meet.
When n is not a multiple of 30, there are no intersections in the interior of an n-gon where more than 5 diagonals meet.
I checked the following conjecture up to n=210: "An n-gon with n=30k has 5n points where 6 or 7 diagonals meet and no points where more than 7 diagonals meet; If k is odd, then 6 diagonals meet in each of 4n points and 7 diagonals meet in each of n points; If k is even, then no groups of exactly 6 diagonals meet in a point, while exactly 7 diagonals meet in each of 5n points."

			a(6)=60 because inside a regular 12-gon there are 60 points (4 on each radius and 1 midway between radii) where exactly three diagonals intersect.

Seiichi Manyama, Table of n, a(n) for n = 2..10000 (terms 2..105 from Graeme McRae)
M. F. Hasler, Interactive illustration of A006561(n)
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, arXiv:math/9508209 [math.MG], 1995-2006, which has fewer typos than the SIAM version.
B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156 (1998). [Copy on SIAM web site]
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998). [Copy on B. Poonen's web site]
B. Poonen and M. Rubinstein, Mathematica programs for A006561 and related sequences
M. Rubinstein, Drawings for n=4,5,6,...
N. J. A. Sloane, Illustrations of a(8) and a(9)
N. J. A. Sloane, Summary table for vertices and regions in regular n-gon with all chords drawn, for n = 3..19. [V = total number of vertices (A007569), V_i (i>=2) = number of vertices where i lines cross (A292105, A292104, A101363); R = total number of cells or regions (A007678), R_i (i>=3) = number of regions with i edges (A331450, A062361, A067151).]
R. G. Wilson V, Illustration of a(10)
Index entry for Sequences formed by drawing all diagonals in regular polygon

Cf. A006561, A007678, A101364, A101365
A column of A292105.
Cf. A000332: C(n, 4) = number of intersection points of diagonals of convex n-gon.
Cf. A006561: number of intersections of diagonals in the interior of regular n-gon
Cf. A292104: number of 2-way intersections in the interior of a regular n-gon
Cf. A101364: number of 4-way intersections in the interior of a regular n-gon
Cf. A101365: number of 5-way intersections in the interior of a regular n-gon
Cf. A137938: number of 4-way intersections in the interior of a regular 6n-gon
Cf. A137939: number of 5-way intersections in the interior of a regular 6n-gon.

A292104 Number of interior points that are the intersections of exactly two chords in the configuration A006561(n).

Original entry on oeis.org

0, 0, 0, 1, 5, 12, 35, 40, 126, 140, 330, 228, 715, 644, 1365, 1168, 2380, 1512, 3876, 3360, 5985, 5280, 8855, 6144, 12650, 11284, 17550, 15680, 23751, 13800, 31465, 28448, 40920, 37264, 52360, 42444, 66045, 60648, 82251, 75720, 101270, 75012, 123410, 114400, 148995, 138644, 178365, 152064

Offset: 1

N. J. A. Sloane, Sep 14 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..120 from Scott R. Shannon)
N. J. A. Sloane, Summary table for vertices and regions in regular n-gon with all chords drawn, for n = 3..19. [V = total number of vertices (A007569), V_i (i>=2) = number of vertices where i lines cross (A292105, A292104, A101363); R = total number of cells or regions (A007678), R_i (i>=3) = number of regions with i edges (A331450, A062361, A067151).]

Cf. A006561. Column k=2 of A292105.

a(31)-a(48) from Scott R. Shannon, Mar 04 2022

A292105 Irregular triangle read by rows: T(n,k) = the number of interior points that are the intersections of exactly k chords in the configuration A006561(n) (n >= 1, k >= 1).

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 5, 0, 12, 1, 0, 35, 0, 40, 8, 1, 0, 126, 0, 140, 20, 0, 1, 0, 330, 0, 228, 60, 12, 0, 1, 0, 715, 0, 644, 112, 0, 0, 0, 1, 0, 1365, 0, 1168, 208, 0, 0, 0, 0, 1, 0, 2380, 0, 1512, 216, 54, 54, 0, 0, 0, 1, 0, 3876, 0, 3360, 480, 0, 0, 0, 0, 0, 0, 1, 0, 5985

Offset: 1

N. J. A. Sloane, Sep 14 2017

			Triangle begins:
  0;
  0;
  0;
  0,   1;
  0,   5;
  0,  12,  1;
  0,  35;
  0,  40,  8,  1;
  0, 126;
  0, 140, 20,  0, 1;
  0, 330;
  0, 228, 60, 12, 0, 1;
See the attached text file for the first 100 rows.

Seiichi Manyama, Rows n = 1..250, flattened
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, arXiv:math/9508209 [math.MG], 1995-2006, which has fewer typos than the SIAM version.
B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156 (1998). [Copy on SIAM web site]
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998). [Copy on B. Poonen's web site]
B. Poonen and M. Rubinstein, Mathematica programs for A006561 and related sequences
N. J. A. Sloane, Summary table for vertices and regions in regular n-gon with all chords drawn, for n = 3..19. [V = total number of vertices (A007569), V_i (i>=2) = number of vertices where i lines cross (A292105, A292104, A101363); R = total number of cells or regions (A007678), R_i (i>=3) = number of regions with i edges (A331450, A062361, A067151).]
N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)
Scott R. Shannon, Table for n=1..100.
Scott R. Shannon, Image of 8-gon.
Scott R. Shannon, Image of 9-gon.
Scott R. Shannon, Image of 12-gon.

Columns give A292104, A101363 (2n-gon), A101364, A101365.
Row sums give A006561.
Cf. A335102.

a(27) and beyond by Scott R. Shannon, May 15 2022

A331449 a(0) = 1 by convention; for n>0, a(n) is the number of points in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter).

Original entry on oeis.org

1, 5, 37, 257, 817, 2757, 4825, 12293, 19241, 33549, 49577, 87685, 101981, 178465, 220113, 286357, 379097, 551669, 606241, 880293, 951445, 1209049, 1507521, 1947877, 2002669, 2624409, 3056093, 3550425, 3955049, 5069037, 5062153, 6669665, 7081969, 8143193, 9365089, 10296469

Offset: 0

N. J. A. Sloane, Jan 23 2020

nonn

Equivalently, this is A334690(n) + 4*n.

Zhao Hui Du, Table of n, a(n) for n = 0..136 (terms 0..52 from Lars Blomberg).
Lars Blomberg, Scott R. Shannon, and N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2021). Also arXiv:2009.07918.
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 20.
Scott R. Shannon, Image for n = 1.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.
Scott R. Shannon, Image for n = 5.
Scott R. Shannon, Image for n = 10.

Cf. A255011, A331448.

For the circular analog see A006533, A007678, A007569, A135565.

By Euler's formula, a(n) = A331448(n) - A255011(n) + 1.

a(11)-a(35) from Giovanni Resta, Jan 28 2020

A344899 Number of polygon edges formed when every pair of vertices of a regular n-gon are joined by an infinite line.

Original entry on oeis.org

0, 1, 3, 8, 30, 78, 189, 320, 684, 1010, 1815, 2052, 3978, 4718, 7665, 8576, 13464, 12546, 22059, 23720, 34230, 36542, 50853, 47928, 72900, 76466, 101439, 105560, 137634, 115230, 182745, 188672, 238128, 245378, 305235, 294948, 385614, 395390, 480909, 491840, 592860, 544950, 723303, 737528

Offset: 1

Scott R. Shannon, Jun 02 2021

nonn

See A344857 for other examples and images of the polygons.

			a(3) = 3 as the connected vertices form a triangle with three edges. Six infinite edges between the outer regions are also formed but these are not counted.
a(5) = 30 as the five connected vertices form a pentagon with fives lines along the pentagon's edges, fifteen lines inside forming eleven polygons, and ten lines outside forming another five triangles. In all these sixteen polygons form thirty edges. Twenty infinite edges between the outer regions are also formed.

J. F. Rigby, Multiple intersections of diagonals of regular polygons, and related topics, Geom. Dedicata 9 (1980), 207-238.
Alexander Sidorenko, Explicit Formulas for Odd-Indexed Terms in A344899, A146212, and A344857.

Cf. A344907 (number of edges for odd n), A344857 (number of polygons), A146212 (number of vertices), A344866, A344311, A007678, A331450, A344938.

Bisections: A344907, A347322.

Conjectured formula odd n: a(n) = (n^4 - 7*n^3 + 17*n^2 - 11*n)/4 = (n-1)*n*(n^2-6*n+11)/4.
This formula is correct: see the Sidorenko link. - N. J. A. Sloane, Sep 12 2021
See also A344907.
a(n) = A344857(n) + A146212(n) - 1 (Euler's theorem.).

A067152 Number of pentagonal regions in regular n-gon with all diagonals drawn.

Original entry on oeis.org

1, 0, 7, 0, 18, 10, 44, 0, 117, 98, 150, 128, 357, 72, 646, 580, 903, 814, 1564, 840, 2050, 2106, 2862, 2128, 3625, 1440, 5146, 4896, 6105, 5542, 8190, 7452, 10471, 10184, 14235, 13160, 16564, 11382, 21156, 20548, 24300, 23920, 30362, 26112, 35231, 32700, 40341, 38532, 51834, 42012, 58905

Offset: 5

Sascha Kurz, Jan 06 2002

nonn

			a(5) = 1 because only the center-region is a pentagon.

B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Scott R. Shannon, Table of n, a(n) for n = 5..765
Sascha Kurz, m-gons in regular n-gons
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998).
Sequences formed by drawing all diagonals in regular polygon

Cf. A007678, A067164, A064869, A067151, A067153, A067154, A067155, A067156, A067157, A067158, A067159.

a(49) and beyond from Scott R. Shannon, Dec 04 2021

Definition clarified by N. J. A. Sloane, Jun 09 2025

A067153 Number of hexagonal regions in regular n-gon with all diagonals drawn.

Original entry on oeis.org

0, 0, 0, 9, 0, 22, 0, 39, 0, 105, 48, 136, 18, 190, 120, 462, 66, 644, 72, 875, 390, 1296, 952, 1595, 450, 1891, 1472, 3201, 2346, 3640, 2124, 4773, 2698, 5577, 4000, 7298, 3444, 7912, 6336, 10980, 6532, 10904, 7824, 14651, 12150, 16779, 13260, 20299, 13176, 21560, 18200, 26961, 21634, 29500

Offset: 6

Sascha Kurz, Jan 06 2002

nonn

			a(9)=9 because drawing the regular 9-gon with all its diagonals yields 9 hexagons.

B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Scott R. Shannon, Table of n, a(n) for n = 6..765
Sascha Kurz, m-gons in regular n-gons
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998).
Sequences formed by drawing all diagonals in regular polygon

Cf. A007678, A067165, A064869, A067151, A067152, A067154, A067155, A067156, A067157, A067158, A067159.

a(54) and beyond from Scott R. Shannon, Dec 04 2021

Definition clarified by N. J. A. Sloane, Jun 09 2025

A350000 Table read by antidiagonals: T(n,k) (n >= 3, k >= 0) is the number of cells in a regular n-gon after k generations of mitosis.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 4, 11, 1, 1, 4, 21, 24, 1, 1, 4, 31, 42, 50, 1, 1, 4, 41, 42, 190, 80, 1, 1, 4, 51, 42, 400, 152, 154, 1, 1, 4, 61, 42, 680, 152, 802, 220, 1, 1, 4, 71, 42, 1030, 152, 1792, 590, 375, 1, 1, 4, 81, 42, 1450, 152, 2962, 690, 2091, 444, 1

Offset: 3

Scott R. Shannon and N. J. A. Sloane, Dec 06 2021

We use "cell" in the sense of planar graph theory, meaning a "region" or two-dimensional face.
We start at generation 0 with a regular n-gon with a single cell.
At each stage the mitosis process splits each cell into smaller cells by drawing chords between every pair of points on the boundary of that cell.
For the first few generations of mitosis of a triangle, square, pentagon, and hexagon, see the sketch in one of the links below.
The process of going from generation 0 to generation 1 was analyzed by Poonen and Rubinstein (1998) - see A007678 and A331450.
It is worth enlarging the illustrations in order to see the detailed structure and the cell counts in the upper left corner. The illustrations for the mitosis of a 7-gon can be seen in A349808 and are not repeated here.
Conjecture 1: For a fixed value of n, there are integers r and s, which are small compared to n, such that T(n,k) is a polynomial in k of degree r for all k >= s.
For example, T(11,k) = 220*k^2 + 1452*k - 1693 for k >= 2. See the Formulas section below for further examples.
Note that if n is odd, all generations of mitosis of a regular n-gon contain a (smaller) regular n-gon at their center.
Conjecture 2: Apart from the central n-gon when n is odd, any cell will eventually split into a mixture of triangles and pentagons.
If we think of triangles and pentagons are harmless cells, and all other cells as dangerous, the conjecture states that (with the exception of the central odd cells), all cells eventually become harmless.

			The table begins:
.
      |               Number of polygons after k generations
  n\k | 0,    1,     2,     3,      4,      5,      6,      7,      8,      9, ...
----------------------------------------------------------------------------------
   3  | 1,    1,     1,     1,      1,      1,      1,      1,      1,      1, ...
   4  | 1,    4,     4,     4,      4,      4,      4,      4,      4,      4, ...
   5  | 1,   11,    21,    31,     41,     51,     61,     71,     81,     91, ...
   6  | 1,   24,    42,    42,     42,     42,     42,     42,     42,     42, ...
   7  | 1,   50,   190,   400,    680,   1030,   1450,   1940,   2500,   3130, ...
   8  | 1,   80,   152,   152,    152,    152,    152,    152,    152,    152, ...
   9  | 1,  154,   802,  1792,   2962,   4312,   5842,   7552,   9442,  11512, ...
  10  | 1,  220,   590,   690,    790,    890,    990,   1090,   1190,   1290, ...
  11  | 1,  375,  2091,  4643,   7635,  11067,  14939,  19251,  24003,  29195, ...
  12  | 1,  444,   948,   948,    948,    948,    948,    948,    948,    948, ...
  13  | 1,  781,  5461, 14119,  24727,  37285,  51793,  68251,  86659, 107017, ...
  14  | 1,  952,  3066,  4046,   5026,   6006,   6986,   7966,   8946,   9926, ...
  15  | 1, 1456,  9361, 22756,  40186,  61066,  85396, 113176, 144406, 179086, ...
  16  | 1, 1696,  6096,  8240,   9520,  10800,  12080,  13360,  14640,  15920, ...
  17  | 1, 2500, 18225, 49131,  90883, 143175, 206007, 279379, 363291, 457743, ...
  18  | 1, 2466,  7344, 10872,  14166,  16866,  19566,  22266,  24966,  27666, ...
  19  | 1, 4029, 29356, 77616, 140316, 217456, 309036, 415056, 535516, 670416, ...
  20  | 1, 4500, 19580, 31620,  39820,  48020,  56220,  64420,  72620,  80820, ...
  21  | 1, 6175, 40720, 97336, 168022, 252778, 351604, 464500, 591466, 732502, ...
  22  | 1, 6820, 31042, 52030,  65890,  79750,  93610, 107470, 121330, 135190, ...
.

B. Poonen and M. Rubinstein, The Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics 11, no. 1 (1998), pp. 135-156; DOI:10.1137/S0895480195281246. [Author's copy]. The latest arXiv version arXiv:math/9508209 has corrected some typos in the published version.
Scott R. Shannon, Extended Table of A350000 for 5 <= n <= 46, Dec 22, 2021 [This shows the initial terms of the rows in human order (not by antidiagonals)]
Scott R. Shannon, Illustration for T(9,1)
Scott R. Shannon, T(9,2)
Scott R. Shannon, T(9,3)
Scott R. Shannon, T(9,4)
Scott R. Shannon, T(10,1)
Scott R. Shannon, T(10,2)
Scott R. Shannon, T(10,3)
Scott R. Shannon, T(11,1)
Scott R. Shannon, T(11,2)
Scott R. Shannon, T(11,3)
Scott R. Shannon, T(14,1)
Scott R. Shannon, T(14,2)
Scott R. Shannon, T(14,3)
Scott R. Shannon, T(17,3)
Scott R. Shannon, T(29,1)
Scott R. Shannon, Close-up of the 11-gon in T(29,1)
Scott R. Shannon, Close-up of a 9-gon in T(29,2). This shows the mitosis of the 11-gon from generation 1 in the previous image -- it has formed one 9-gon, five 7-gons, twelve 6-gons and numerous other 5, 4, and 3-gons.
Scott R. Shannon, Zoomed-in view of T(51,2). This shows the complicated structure formed after just 2 generations, typical of larger values of n.
N. J. A. Sloane, Rough sketch of first few generations of mitosis of a triangle, square, pentagon, and hexagon. The central pentagonal cell of the pentagon splits into 10 triangles and a pentagon at every generation, with the cells getting smaller and smaller. The third splitting is drawn in red ink. The second splitting of the hexagon is also drawn in red ink, but then all the cells are triangles, and no further mitosis takes place.

Cf. A007678 (column 1), A349807 (column 2), A017281 (row 5), A349808 (row 7); also A350501, A350502.

Cf. also A331450, A349967, A349968.

Formulas for the initial rows: (These are easy to prove.)
To avoid double subscripts, we use a(k) for T(n,k) when we are looking at row n.
n=3: a(k) = 1, for k >= 0.
n=4: a(0) = 1, a(k) = 4 for k >= 1.
n=5: a(k) = 10k+1, k >= 0. See A017281.
n=6: a(0) = 1, a(1) = 24, a(k) = 42 for k >= 2.
n=7: a(0) = 1, a(k) = 35*k^2+35*k-20 for k >= 1. See A349808.
n=8: a(0) = 1, a(1) = 80, a(k) = 152 for k >= 2.
n=9: a(0) = 1, a(1) = 154, a(k) = 90*k^2+540*k-638 for k >= 2.
n=10: a(0) = 1, a(1) = 220, a(k) = 100*k+390 for k >= 2.
n=11: a(0) = 1, a(1) = 375, a(k) = 220*k^2 + 1452*k - 1693 for k >= 2.
n=12: a(0) = 1, a(1) = 444, a(k) = 948 for k >= 2.
n=13: a(0) = 1, a(1) = 781, a(k) = 975*k^2 + 3783*k - 6005 for k >= 2.
n=14: a(0) = 1, a(k) = 980*k + 1106 for k >= 1.
n=15: a(k) = 1725*k^2+5355*k-8834 for k >= 3.
n=16: a(k) = 1280*k + 4400 for k >= 3.
n=18: a(k) = 2700*k + 3366 for k >= 4.
Also T(n,1) = A007678(n).

A067154 Number of heptagonal regions in regular n-gon with all diagonals drawn.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 15, 0, 17, 18, 57, 0, 21, 44, 115, 0, 150, 104, 81, 112, 116, 0, 155, 224, 429, 306, 560, 180, 555, 836, 663, 640, 1025, 378, 1419, 660, 1710, 1564, 1786, 1200, 2352, 1050, 2754, 2236, 2597, 2700, 3410, 2240, 3078, 3190, 4602, 1860, 5551, 4898, 6363, 5056, 8515, 4950

Offset: 7

Sascha Kurz, Jan 06 2002

nonn

			a(7)=1 because the center-region is a heptagon.

B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Scott R. Shannon, Table of n, a(n) for n = 7..765
Sascha Kurz, m-gons in regular n-gons
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998).
Sequences formed by drawing all diagonals in regular polygon

Cf. A007678, A067166, A064869, A067151, A067152, A067153, A067155, A067156, A067157, A067158, A067159.

a(62) and beyond from Scott R. Shannon, Dec 04 2021

Definition clarified by N. J. A. Sloane, Jun 09 2025

A067155 Number of octagonal regions in regular n-gon with all diagonals drawn.

Original entry on oeis.org

0, 0, 0, 0, 0, 13, 0, 0, 0, 34, 0, 38, 20, 0, 44, 23, 0, 50, 26, 108, 28, 145, 0, 217, 0, 264, 102, 315, 72, 407, 190, 546, 200, 656, 42, 903, 528, 810, 598, 1175, 288, 1078, 550, 1479, 780, 1166, 486, 1705, 784, 2451, 1276, 3068, 960, 3172, 1860, 4347, 2432, 4225, 2376, 4958, 2992, 3519, 2380

Offset: 8

Sascha Kurz, Jan 06 2002

nonn

			a(13)=13 because drawing the regular 13-gon and all its diagonals yields 13 octagons.

B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Scott R. Shannon, Table of n, a(n) for n = 8..765
Sascha Kurz, m-gons in regular n-gons
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998).
Sequences formed by drawing all diagonals in regular polygon

Cf. A007678, A067167, A064869, A067151, A067152, A067153, A067154, A067156, A067157, A067158, A067159.

a(65) and beyond from Scott R. Shannon, Dec 04 2021

Definition clarified by Hugo Pfoertner, Dec 04 2021

cp's OEIS Frontend

A101363 In the interior of a regular 2n-gon with all diagonals drawn, the number of points where exactly three diagonals intersect.

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A292104 Number of interior points that are the intersections of exactly two chords in the configuration A006561(n).

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A292105 Irregular triangle read by rows: T(n,k) = the number of interior points that are the intersections of exactly k chords in the configuration A006561(n) (n >= 1, k >= 1).

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A331449 a(0) = 1 by convention; for n>0, a(n) is the number of points in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter).

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A344899 Number of polygon edges formed when every pair of vertices of a regular n-gon are joined by an infinite line.

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A067152 Number of pentagonal regions in regular n-gon with all diagonals drawn.

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A067153 Number of hexagonal regions in regular n-gon with all diagonals drawn.

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A350000 Table read by antidiagonals: T(n,k) (n >= 3, k >= 0) is the number of cells in a regular n-gon after k generations of mitosis.

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A067154 Number of heptagonal regions in regular n-gon with all diagonals drawn.

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A067155 Number of octagonal regions in regular n-gon with all diagonals drawn.

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