A331909 - OEIS

%I #16 May 10 2020 14:55:53

%S 132,36,0,0,2052,1188,324,24,0,10440,7956,1728,300,0,0,33672,28812,

%T 9276,1836,228,24,12,83040,75276,24948,5436,708,60,0,0,172140,162060,

%U 54732,11280,1836,168,0,0,0,322284,315492,114624,25980,3948,456,24,0,0,0

%N 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.

%C See the links in A331908 for images of the hexagrams.

%H Lars Blomberg, <a href="/A331909/b331909.txt">Table of n, a(n) for n = 1..319</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hexagram.html">Hexagram</a>.

%e 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].

%e Triangle begins:

%e   132, 36, 0, 0

%e   2052, 1188, 324, 24, 0

%e   10440, 7956, 1728, 300, 0, 0

%e   33672, 28812, 9276, 1836, 228, 24, 12

%e   83040, 75276, 24948, 5436, 708, 60, 0, 0

%e The row sums are A331908.

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

%K nonn,tabf

%O 1,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 31 2020

%E a(31) and beyond from _Lars Blomberg_, May 10 2020