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.

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

Author

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

Keywords

• nonn
• tabf

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

• Lars Blomberg, Table of n, a(n) for n = 1..241 (the first 23 rows)

Crossrefs

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

Extensions

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