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A286482 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. 0

%I

%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 that 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 octogons are:

%e [2,3,1,1,4,4,2,3] and [3,2,4,4,1,1,3,2]:

%e xx

%e x x

%e x x

%e xx

%e [2,3,1,4,1,4,2,3] and [3,2,4,1,4,1,3,2]:

%e x x

%e x x

%e x x

%e x x

%e [2,3,1,4,4,1,3,2] and [3,2,4,1,1,4,2,3]:

%e xx

%e x x

%e x x

%e x x

%Y Cf. A285521.

%K nonn,more

%O 1,3

%A _Peter Kagey_, May 12 2017

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Last modified August 20 06:04 EDT 2019. Contains 326139 sequences. (Running on oeis4.)