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%I #27 Jan 11 2020 03:08:41
%S 1,1,6,6,26,12,42,6,24,2,48,2,64,2,56
%N The number of convex n-gons with vertices consisting of pairs of positive integers (1, s_1), ..., (n, s_n) such that max(s_i) is minimized.
%C a(n) is even for all n > 2 because an n-gon whose vertices are defined by a function cannot have vertical symmetry, thus each polygon has a corresponding polygon which is flipped vertically.
%C For each n-gon, max(s_i) is equal to the maximum value in the n-th row of A285521.
%e For n = 8, the a(8) = 6 octagons are depicted below as three pairs, with the polygons on top being a vertical reflection of the polygons below (and vice versa).
%e .
%e . [2,3,1,1,4,4,2,3] [2,3,1,4,1,4,2,3] [2,3,1,4,4,1,3,2]
%e .
%e . xx x x xx
%e . x x x x x x
%e . x x x x x x
%e . xx x x x x
%e .
%e .----------------------------------------------------------
%e .
%e . xx x x x x
%e . x x x x x x
%e . x x x x x x
%e . xx x x xx
%e .
%e . [3,2,4,4,1,1,3,2] [3,2,4,1,4,1,3,2] [3,2,4,1,1,4,2,3]
%Y Cf. A285521.
%K nonn,more
%O 1,3
%A _Peter Kagey_, May 12 2017
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