A331932 Triangle read by rows: Take a hexagon with all diagonals drawn, as in A331931. Then T(n,k) = number of k-sided polygons in that figure for k = 3, 4, ..., n+4.

18, 6, 0, 264, 108, 36, 0, 1344, 654, 252, 12, 6, 4164, 2772, 1020, 228, 24, 0, 10038, 7758, 2424, 516, 72, 24, 0, 21108, 16188, 6060, 1128, 156, 0, 0, 0, 39690, 32022, 13368, 3654, 432, 48, 0, 0, 0, 68052, 56616, 22980, 6084, 888, 120, 12, 0, 0, 0

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Feb 01 2020

Keywords

• nonn
• tabf

Comments

See the links in A331931 for images of the hexagons.

Examples

			A hexagon with no other points along its edges, n = 1, contains 18 triangles, 6 quadrilaterals and no other n-gons, so the first row is [18,6,0]. A hexagon with 1 point dividing its edges, n = 2, contains 264 triangles, 108 quadrilaterals, 36 pentagons and no other n-gons, so the second row is [264,108,36,0].
Triangle begins:
  18,6,0
  264,108,36,0
  1344,654,252,12,6
  4164,2772,1020,228,24,0
  10038,7758,2424,516,72,24,0
  21108,16188,6060,1128,156,0,0,0
  39690,32022,13368,3654,432,48,0,0,0
  68052,56616,22980,6084,888,120,12,0,0,0
The row sums are A331931.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..525 (the first 30 rows)
• Wikipedia, Hexagon.

Crossrefs

Cf. A331931 (regions), A330845 (edges), A330846 (vertices), A331906, A007678, A092867, A331452.