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A366486 Place n equally spaced points on each side of an equilateral triangle, and join each of these points by a chord to the 2*n new points on the other two sides: sequence gives number of regions in the resulting planar graph.

%I A366486 #21 Nov 12 2023 00:07:16
%S A366486 1,4,27,130,385,1044,2005,4060,6831,11272,16819,26436,35737,52147,
%T A366486 69984,92080,117952,157770,193465,249219,302670,368506,443026,546462,
%U A366486 635125,757978,890133,1041775,1191442,1407324,1581058,1837417,2085096,2365657,2670429,3018822,3328351,3771595,4213602
%N A366486 Place n equally spaced points on each side of an equilateral triangle, and join each of these points by a chord to the 2*n new points on the other two sides: sequence gives number of regions in the resulting planar graph.
%C A366486 See A366483 for further information.
%H A366486 Scott R. Shannon, <a href="/A366486/a366486.png">Image for n = 1</a>.
%H A366486 Scott R. Shannon, <a href="/A366486/a366486_1.png">Image for n = 2</a>.
%H A366486 Scott R. Shannon, <a href="/A366486/a366486_2.png">Image for n = 3</a>.
%H A366486 Scott R. Shannon, <a href="/A366486/a366486_3.png">Image for n = 4</a>.
%H A366486 Scott R. Shannon, <a href="/A366486/a366486_4.png">Image for n = 5</a>.
%H A366486 Scott R. Shannon, <a href="/A366486/a366486_5.png">Image for n = 10</a>.
%F A366486 a(n) = A366485(n) - A366483(n) + 1 (Euler).
%Y A366486 Cf. A366483 (vertices), A366484 (interior vertices), A366485 (edges).
%Y A366486 If the 3*n points are placed "in general position" instead of uniformly, we get sequences A366478, A365929, A366932, A367015.
%Y A366486 If the 3*n points are placed uniformly and we also draw chords from the three corner points of the triangle to these 3*n points, we get A274585, A092866, A274586, A092867.
%K A366486 nonn
%O A366486 0,2
%A A366486 _Scott R. Shannon_ and _N. J. A. Sloane_, Nov 09 2023