%I #26 Nov 07 2023 08:24:48
%S 1,3,10,58,178,558,1255,2532,4786,7804,12292,18966,28540,39117,56107,
%T 73924,96010,124704,164815,203316,258706,311296,377998,458862,560827,
%U 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 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 Total number of points at intersections of sides/"chords" for the triangle in A092866(n).
%H Scott R. Shannon, <a href="/A274585/a274585.png">Image for n = 2</a>.
%H Scott R. Shannon, <a href="/A274585/a274585_1.png">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A274585/a274585_2.png">Image for n = 4</a>.
%H Scott R. Shannon, <a href="/A274585/a274585_3.png">Image for n = 5</a>.
%H Scott R. Shannon, <a href="/A274585/a274585_4.png">Image for n = 6</a>.
%H Scott R. Shannon, <a href="/A274585/a274585_5.png">Image for n = 10</a>.
%F a(n) = A092866(n) + 3n.
%F By the Euler characteristic, a(n) = A274586(n) - A092867(n) + 1.
%Y Cf. A092866, A092867, A274586.
%K nonn
%O 0,2
%A _Cynthia Miaina Rasamimanananivo_ and _Max Alekseyev_, Jun 29 2016, Sep 02 2016
%E a(0) = 1 added by _N. J. A. Sloane_, Jan 22 2022