A347751 Number of finite edges in the graph formed when every pair of vertices of a row of n adjacent congruent rectangles are joined by an infinite line.

0, 8, 36, 124, 300, 664, 1200, 2108, 3388, 5232, 7568, 10852, 14892, 20288, 26704, 34540, 43812, 55400, 68584, 84684, 103004, 124216, 147888, 175820, 206788, 242424, 281560, 325708, 374148, 429416, 489000, 556412, 629804, 710536, 797280, 892564, 994588, 1107744, 1228432, 1359292, 1498788

Offset: 0

Author

Scott R. Shannon and N. J. A. Sloane, Sep 12 2021

Keywords

• nonn

Comments

See A344993 and A347750 for images of the rectangles.

Examples

			a(1) = 8 as connecting the four vertices of a single rectangle forms four new edges inside the rectangle, giving a total of 4 + 4 = 8 total edges.
a(2) = 36 as connecting the six vertices of two adjacent rectangles forms twenty-two edges inside the rectangles while also forming eight edges outside the rectangles. The total number of edges is then 6 + 22 + 8 = 36.
		

Crossrefs

Cf. A344993 (number of polygons), A347750 (number of intersections), A331757 (number of edges on or inside the rectangles).

Formula

a(n) = A344993(n) + A347750(n) - 1.