A344279 - OEIS

%I #44 Jul 21 2021 09:09:15

%S 1,12,102,396,1198,2748,5539,10272,16986,26934,41179,60804,84769,

%T 119022,157947,206352,268030,347430,432820,543210,659238,801804,

%U 970429,1171662,1371040,1627398,1904550,2213712,2555320,2971260,3373399,3881838,4399329,4988502,5610543,6315312

%N Number of polygons formed by infinite lines when connecting all vertices and all points that divide the sides of an equilateral triangle into n equal parts.

%H Scott R. Shannon, <a href="/A344279/a344279.gif">Image for n = 2</a>. In this and other images the triangle's points are highlighted as white dots while the outer open regions, which are not counted, are darkened. The key for the edge-number coloring is shown at the top-left of the image.

%H Scott R. Shannon, <a href="/A344279/a344279_1.gif">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A344279/a344279_2.gif">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A344279/a344279_3.gif">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A344279/a344279_4.gif">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A344279/a344279_5.gif">Image for n = 7</a>.

%H Scott R. Shannon, <a href="/A344279/a344279_6.gif">Image for n = 8</a>.

%F a(n) = A344896(n) - A344657(n) + 1.

%Y Cf. A344657 (number of vertices), A344896 (number of edges), A346446 (number of k-gons), A092867 (number polygons inside the triangle),  A343755 (number of regions), A345459, A344857.

%K nonn

%O 1,2

%A _Scott R. Shannon_, Jun 22 2021