cp's OEIS Frontend

A367118 Place n points in general position on each side of an equilateral triangle, and join every pair of the 3*n+3 boundary points by a chord; sequence gives number of regions in the resulting planar graph.

%I A367118 #19 Nov 09 2023 03:28:34
%S A367118 1,13,82,307,841,1891,3718,6637,11017,17281,25906,37423,52417,71527,
%T A367118 95446,124921,160753,203797,254962,315211,385561,467083,560902,668197,
%U A367118 790201,928201,1083538,1257607,1451857,1667791,1906966,2170993,2461537,2780317,3129106,3509731,3924073,4374067
%N A367118 Place n points in general position on each side of an equilateral triangle, and join every pair of the 3*n+3 boundary points by a chord; sequence gives number of regions in the resulting planar graph.
%C A367118 "In general position" implies that the internal lines (or chords) only have simple intersections. There is no interior point where three or more chords meet.
%H A367118 Scott R. Shannon, <a href="/A367118/a367118.png">Image for n = 1</a>.
%H A367118 Scott R. Shannon, <a href="/A367118/a367118_1.png">Image for n = 2</a>.
%H A367118 Scott R. Shannon, <a href="/A367118/a367118_2.png">Image for n = 5</a>.
%F A367118 Conjecture: a(n) = (1/4)*(9*n^4 + 12*n^3 + 15*n^2 + 12*n + 4).
%F A367118 a(n) = A367119(n) - A367117(n) + 1 by Euler's formula.
%Y A367118 Cf. A367117 (vertices), A367119 (edges), A091908, A092098, A331782, A367015.
%Y A367118 If the boundary points are equally spaced, we get A274585, A092866, A274586, A092867. - _N. J. A. Sloane_, Nov 09 2023
%K A367118 nonn
%O A367118 0,2
%A A367118 _Scott R. Shannon_ and _N. J. A. Sloane_, Nov 05 2023