A331909 Triangle read by rows: Take a hexagram with all diagonals drawn, as in A331908. Then T(n,k) = number of k-sided polygons in that figure for k = 3, 4, ..., n+5.

132, 36, 0, 0, 2052, 1188, 324, 24, 0, 10440, 7956, 1728, 300, 0, 0, 33672, 28812, 9276, 1836, 228, 24, 12, 83040, 75276, 24948, 5436, 708, 60, 0, 0, 172140, 162060, 54732, 11280, 1836, 168, 0, 0, 0, 322284, 315492, 114624, 25980, 3948, 456, 24, 0, 0, 0

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Jan 31 2020

Keywords

• nonn
• tabf

Comments

See the links in A331908 for images of the hexagrams.

Examples

			A hexagram with no other points along its edges, n = 1, contains 132 triangles, 36 quadrilaterals and no other n-gons, so the first row is [132,36,0,0]. A hexagram with 1 point dividing its edges, n = 2, contains 2052 triangles, 1188 quadrilaterals, 324 pentagons, 24 hexagons and no other n-gons, so the second row is [2052,1188,324,24,0].
Triangle begins:
  132, 36, 0, 0
  2052, 1188, 324, 24, 0
  10440, 7956, 1728, 300, 0, 0
  33672, 28812, 9276, 1836, 228, 24, 12
  83040, 75276, 24948, 5436, 708, 60, 0, 0
The row sums are A331908.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..319
• Eric Weisstein's World of Mathematics, Hexagram.

Crossrefs

Cf. A331908 (regions), A333116 (vertices), A333049 (edges), A007678, A092867, A331452, A331906.

Extensions

a(31) and beyond from Lars Blomberg, May 10 2020