%I #10 Sep 12 2021 08:21:38
%S 0,5,17,57,133,297,525,925,1477,2289,3277,4701,6437,8805,11541,14917,
%T 18869,23893,29509,36473,44349,53545,63605,75629,88901,104325,120981,
%U 139913,160581,184409,209885,238989,270525,305413,342413,383301,426949,475757,527205,583261,642821,708717,777829
%N Number of intersection points when every pair of vertices of a row of n adjacent congruent rectangles are joined by an infinite line.
%H Scott R. Shannon, <a href="/A347750/a347750.png">Image for n = 2</a>.
%H Scott R. Shannon, <a href="/A347750/a347750_1.png">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A347750/a347750_2.png">Image for n = 4</a>.
%H Scott R. Shannon, <a href="/A347750/a347750_3.png">Image for n = 5</a>.
%H Scott R. Shannon, <a href="/A347750/a347750_4.png">Image for n = 6</a>.
%F a(n) = A347751(n) - A344993(n) + 1.
%e a(1) = 5 as connecting the four vertices of a single rectangle forms one new vertex inside the rectangle, giving a total of 4 + 1 = 5 total intersection points.
%e a(2) = 17 as connecting the six vertices of two adjacent rectangles forms seven vertices inside the rectangles while also forming four vertices outside the rectangles. The total number of intersection points is then 6 + 7 + 4 = 17.
%e See the linked images for further examples.
%Y Cf. A344993 (number of polygons), A347751 (number of edges), A331755 (number of intersections on or inside the rectangles).
%K nonn
%O 0,2
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Sep 12 2021