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%I #21 Oct 21 2022 14:59:44
%S 8,12,18,16,64,32,20,150,200,50,24,288,720,480,72,28,490,1960,2450,
%T 980,98,32,768,4480,8960,6720,1792,128,36,1134,9072,26460,31752,15876,
%U 3024,162,40,1600,16800,67200,117600,94080,33600,4800,200,44,2178,29040,152460,365904,426888,243936,65340,7260,242
%N Triangle read by rows: T(n,k) = number of vertices of degree k in an origami flip graph OFG(A2n).
%C See page 2 of Hull, et al. (2022) for a description of OFG(A_2n).
%H Michael De Vlieger, <a href="/A352880/b352880.txt">Table of n, a(n) for n = 2..11176</a> (rows 2..150, flattened)
%H Thomas C. Hull, Manuel Morales, Sarah Nash, and Natalya Ter-Saakov, <a href="https://arxiv.org/abs/2203.14173">Maximal origami flip graphs of flat-foldable vertices: properties and algorithms</a>, arXiv:2203.14173 [math.CO], 2022, p. 13.
%F T(n,k) = (4n/(n+1)) * binomial(n+1, k-n-1) * binomial(n-2, k-n-2) for n+2 <= k <= 2n.
%e Table begins:
%e 2n\k | 4 5 6 7 8 9 10 11 12
%e ---------------------------------------------
%e 4 | 8
%e 6 | 12 18
%e 8 | 16 64 32
%e 10 | 20 150 200 50
%e 12 | 24 288 720 480 72
%e ...
%t Table[(4 n/(n + 1)) Binomial[n + 1, k - n - 1] Binomial[n - 2, k - n - 2], {n, 2, 11}, {k, n + 2, 2 n}] // Flatten
%K nonn,tabl,easy
%O 2,1
%A _Michael De Vlieger_, Apr 06 2022