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A366484 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 interior vertices in the resulting planar graph.

%I A366484 #23 Jul 09 2025 05:02:58
%S A366484 0,0,13,96,285,901,1605,3534,5797,9813,14319,23809,30912,47154,62728,
%T A366484 82440,104493,144730,173637,229948,276325,336861,403383,509146,582342,
%U A366484 702150,824875,969303,1098225,1321888,1463487,1724094,1952410,2221395,2505064,2846800,3103677,3556029,3978646,4443883
%N A366484 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 interior vertices in the resulting planar graph.
%C A366484 See A366483 for further information.
%H A366484 Scott R. Shannon, <a href="/A366484/a366484.png">Image for n = 2</a>.
%H A366484 Scott R. Shannon, <a href="/A366484/a366484_1.png">Image for n = 3</a>.
%H A366484 Scott R. Shannon, <a href="/A366484/a366484_2.png">Image for n = 4</a>.
%H A366484 Scott R. Shannon, <a href="/A366484/a366484_3.png">Image for n = 5</a>.
%H A366484 Scott R. Shannon, <a href="/A366484/a366484_4.png">Image for n = 10</a>.
%F A366484 a(n) = A366485(n) - A366486(n) - 3*n - 2 (Euler).
%Y A366484 Cf. A366483 (vertices), A366485 (edges), A366486 (regions).
%Y A366484 If the 3*n points are placed "in general position" instead of uniformly, we get sequences A366478, A365929, A366932, A367015.
%Y A366484 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 A366484 nonn
%O A366484 0,3
%A A366484 _Scott R. Shannon_ and _N. J. A. Sloane_, Nov 09 2023