This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347750 #15 Jul 04 2025 12:37:28 %S A347750 0,5,17,57,133,297,525,925,1477,2289,3277,4701,6437,8805,11541,14917, %T A347750 18869,23893,29509,36473,44349,53545,63605,75629,88901,104325,120981, %U A347750 139913,160581,184409,209885,238989,270525,305413,342413,383301,426949,475757,527205,583261,642821,708717,777829 %N A347750 Number of intersection points when every pair of vertices of a row of n adjacent congruent rectangles are joined by an infinite line. %H A347750 Scott R. Shannon, <a href="/A347750/a347750.png">Image for n = 2</a>. %H A347750 Scott R. Shannon, <a href="/A347750/a347750_1.png">Image for n = 3</a>. %H A347750 Scott R. Shannon, <a href="/A347750/a347750_2.png">Image for n = 4</a>. %H A347750 Scott R. Shannon, <a href="/A347750/a347750_3.png">Image for n = 5</a>. %H A347750 Scott R. Shannon, <a href="/A347750/a347750_4.png">Image for n = 6</a>. %F A347750 a(n) = A347751(n) - A344993(n) + 1. %F A347750 It seems that a(n) = 2 * A159065(n+1) + 3 for n>0. - _Andrei Zabolotskii_, Jul 03 2025 %e A347750 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 A347750 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 A347750 See the linked images for further examples. %Y A347750 Cf. A344993 (number of polygons), A347751 (number of edges), A159065, A331755, A092275 (number of intersections resp. inside the rectangles, on or inside them, above them). %K A347750 nonn %O A347750 0,2 %A A347750 _Scott R. Shannon_ and _N. J. A. Sloane_, Sep 12 2021