A332723 Irregular table read by rows: Take a line with n equally spaced points with semicircles drawn between them, as in A290447. Then T(n,k) = number of k-sided regions in that figure, where k>=2.

1, 2, 1, 3, 4, 4, 10, 0, 1, 5, 19, 3, 3, 6, 31, 13, 6, 7, 46, 35, 10, 8, 65, 74, 14, 9, 92, 131, 18, 10, 140, 192, 27, 1, 11, 202, 274, 46, 3, 12, 275, 396, 62, 3, 13, 363, 563, 79, 9, 14, 467, 784, 100, 14, 15, 598, 1054, 126, 12, 2

Offset: 2

Author

Scott R. Shannon and N. J. A. Sloane, Feb 21 2020

Keywords

• nonn
• tabf

Examples

			The first 25 rows are:
1;
2,1;
3,4;
4,10,0,1;
5,19,3,3;
6,31,13,6;
7,46,35,10;
8,65,74,14;
9,92,131,18;
10,140,192,27,1;
11,202,274,46,3;
12,275,396,62,3;
13,363,563,79,9;
14,467,784,100,14;
15,598,1054,126,12,2;
16,772,1358,159,13,2;
17,996,1698,216,24,2,1;
18,1255,2120,266,41,2;
19,1551,2629,346,54,5;
20,1892,3236,425,71,8;
21,2304,3909,525,83,9,1;
22,2793,4676,629,108,9,2;
23,3342,5559,792,125,14,3;
24,3982,6546,948,166,15,2;
25,4705,7658,1145,198,14,3;
The row sums are A290865.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 2..345. The terms for 2 to 55 points.
• Scott R. Shannon, Illustration of regions for n = 5.
• Scott R. Shannon, Illustration of regions for n = 6.
• Scott R. Shannon, Illustration of regions for n = 10.
• Scott R. Shannon, Illustration of regions for n = 11.
• Scott R. Shannon, Illustration of regions for n = 15.
• Scott R. Shannon, Illustration of regions for n = 16.
• Scott R. Shannon, Illustration of regions for n = 20.
• Scott R. Shannon, Illustration of regions for n = 21.
• Scott R. Shannon, Illustration of regions for n = 25.
• Scott R. Shannon, Illustration of regions for n = 26.
• Scott R. Shannon, Illustration of regions with random distance-based coloring for n = 10.
• Scott R. Shannon, Illustration of regions with random distance-based coloring for n = 11.
• Scott R. Shannon, Illustration of regions with random distance-based coloring for n = 15.
• Scott R. Shannon, Illustration of regions with random distance-based coloring for n = 16.
• Scott R. Shannon, Illustration of regions with random distance-based coloring for n = 20.
• Scott R. Shannon, Illustration of regions with random distance-based coloring for n = 21.
• Scott R. Shannon, Illustration of regions with random distance-based coloring for n = 25.
• Scott R. Shannon, Illustration of regions with random distance-based coloring for n = 26.

Crossrefs

Cf. A290447, A290865, A290866, A290867, A290726.