A331909 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See the links in A331908 for images of the hexagrams.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..319

Eric Weisstein's World of Mathematics, Hexagram.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A263299 A330202 A243832 * A001295 A105684 A211407

Adjacent sequences: A331906 A331907 A331908 * A331910 A331911 A331912

KEYWORD

nonn,tabf

AUTHOR

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

EXTENSIONS

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

STATUS

approved