A331908
The number of regions inside a hexagram formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
Original entry on oeis.org
168, 3588, 20424, 73860, 189468, 402216, 782808, 1385040, 2214108, 3423840, 5196312, 7218552, 10353432, 13823772, 18047124, 24083736, 31051152, 38334972, 48877440, 59201544, 72052956, 88004184, 106601088, 124009020
Offset: 1
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.
Original entry on oeis.org
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
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.
A333049
The number of edges inside a hexagram formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
Original entry on oeis.org
276, 6348, 36810, 137802, 356538, 760134, 1494702, 2668458, 4254294, 6597690, 10105662, 13949346, 20222142, 26925654, 35032086, 47139258, 60947286, 74831682, 96101142, 115904808, 141052560, 172931484, 210293622, 243217686
Offset: 1
A338003
The number of vertices in a 4-pointed star formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
Original entry on oeis.org
37, 653, 5517, 17153, 50349, 97037, 204329, 330613, 571021, 835713, 1298533, 1764125
Offset: 1
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