A335861 Number of regions in a Y-shaped polygon with equal arms of length n (see the Comments for definition).

1, 70, 349, 916, 1474, 2296, 3412, 4978, 7042, 9748, 13132, 17506, 22786, 29410, 37288, 46630, 57574

Offset: 0

Author

Scott R. Shannon and N. J. A. Sloane, Sep 22 2020

Keywords

• nonn
• more

Comments

This polygon consists of a central equilateral triangle with a line of n adjacent squares connected to each of its three edges. This gives the polygon a total of one triangle, 3n squares, and 6n+3 vertices. Join every pair of vertices by a line segment, provided the line does not extend beyond the boundary of the polygon. The sequence gives the number of regions in the resulting figure.

Examples

			a(0) = 1. There is one region in an equilateral triangle with no other polygons.
a(1) = 70. With one square adjacent to each of the triangles sides the resulting line segments form 48 triangles, twelves 4-gons, nine 5-gons, and one 6-gon. This gives a total of 70 regions. See the first linked image.
		

Links

• Scott R. Shannon, Image for the figure with edge-count coloring for n=1.
• Scott R. Shannon, Image for the figure with edge-count coloring for n=2.
• Scott R. Shannon, Image for the figure with edge-count coloring for n=3.
• Scott R. Shannon, Image for the figure with edge-count coloring for n=4.
• Scott R. Shannon, Image for the figure with edge-count coloring for n=5.
• Scott R. Shannon, Image for the figure with edge-count coloring for n=6.

Crossrefs

Cf. A337790 (number of vertices), A331456, A331452, A306302, A092867, A007678.