A332417 Irregular table read by rows: Take a decagon with all diagonals drawn, as in A333139. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.

120, 90, 10, 2040, 1580, 460, 140, 10860, 8570, 4170, 1380, 210, 20, 10, 34360, 30420, 14240, 4020, 1120, 100, 20, 85600, 76920, 38610, 13360, 2650, 550, 110, 176760, 166400, 82560, 24500, 5500, 760, 140, 20, 327550, 320520, 159860, 51610, 10960, 2250, 300, 30, 0, 10

Offset: 1

Author

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

Keywords

• nonn
• tabf

Comments

See the links in A333139 for images of the decagons.

Examples

			A decagon with no other points along its edges, n = 1, contains 120 triangles, 90 quadrilaterals, 10 pentagons and no other n-gons, so the first row is [120, 90, 10]. A decagon with 1 point dividing its edges, n = 2, contains 2040 triangles, 1580 quadrilaterals, 460 pentagons, 140 hexagons and no other n-gons, so the second row is [2040,1580,460,140].
Table begins:
120, 90, 10;
2040,1580,460,140;
10860,8570,4170,1380,210,20,10;
34360,30420,14240,4020,1120,100,20;
85600,76920,38610,13360,2650,550,110;
176760, 166400, 82560, 24500, 5500, 760, 140, 20;
327550, 320520, 159860, 51610, 10960, 2250, 300, 30, 0, 10;
565060, 549520, 277360, 86540, 18960, 3560, 480, 20, 20;
910920, 891290, 447790, 147300, 32180, 5640, 720, 130, 40, 10;
The row sums are A333139.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..181 (the first 21 rows)

Crossrefs

Cf. A333139 (regions), A332418 (vertices), A332419 (edges), A007678, A092867, A331452, A331929.

Extensions

a(29) and beyond from Lars Blomberg, May 18 2020