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%I #19 Sep 10 2022 21:04:57
%S 3,9,27,57,99,135,219,297,351,489,603,645,867,1017,1107,1353,1539,
%T 1575,1947,2127,2295,2649,2907,3021,3459,3753,3855,4359,4707,4821,
%U 5403,5769,5967,6537,6897,6957,7779,8217,8451,9003,9603,9837,10587,11061,11211,12153,12699,12897,13827,14409,14715
%N Number of edges in an equilateral triangle when n internal equilateral triangles are drawn between the 3n points that divide each side into n+1 equal parts.
%C See A356984 and A357007 for images of the triangles.
%H Scott R. Shannon, <a href="/A357008/b357008.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = A356984(n) + A357007(n) - 1 by Euler's formula.
%F Conjecture: a(n) = 6*n^2 + 3 for equilateral triangles that only contain simple vertices when cut by n internal equilateral triangles. This is never the case if (n + 1) mod 3 = 0 for n > 3.
%Y Cf. A356984 (regions), A357007 (vertices), A274586, A332376, A333027, A344896.
%K nonn
%O 0,1
%A _Scott R. Shannon_, Sep 08 2022