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 A274585 #26 Nov 07 2023 08:24:48 %S A274585 1,3,10,58,178,558,1255,2532,4786,7804,12292,18966,28540,39117,56107, %T A274585 73924,96010,124704,164815,203316,258706,311296,377998,458862,560827, %U A274585 649011,775336,908974,1056604,1215174,1428283,1607964,1866103,2111587,2399647,2694115,3040309,3356544,3811501,4253191,4720222,5180589,5806813,6325035,7036081,7691035,8392174,9180471,10136431,10894698,11930983 %N A274585 Total number of vertices formed by intersections among sides and straight "chords" in a right triangle when each side is divided by vertices into n equal segments. %C A274585 Total number of points at intersections of sides/"chords" for the triangle in A092866(n). %H A274585 Scott R. Shannon, <a href="/A274585/a274585.png">Image for n = 2</a>. %H A274585 Scott R. Shannon, <a href="/A274585/a274585_1.png">Image for n = 3</a>. %H A274585 Scott R. Shannon, <a href="/A274585/a274585_2.png">Image for n = 4</a>. %H A274585 Scott R. Shannon, <a href="/A274585/a274585_3.png">Image for n = 5</a>. %H A274585 Scott R. Shannon, <a href="/A274585/a274585_4.png">Image for n = 6</a>. %H A274585 Scott R. Shannon, <a href="/A274585/a274585_5.png">Image for n = 10</a>. %F A274585 a(n) = A092866(n) + 3n. %F A274585 By the Euler characteristic, a(n) = A274586(n) - A092867(n) + 1. %Y A274585 Cf. A092866, A092867, A274586. %K A274585 nonn %O A274585 0,2 %A A274585 _Cynthia Miaina Rasamimanananivo_ and _Max Alekseyev_, Jun 29 2016, Sep 02 2016 %E A274585 a(0) = 1 added by _N. J. A. Sloane_, Jan 22 2022