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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 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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Last modified May 27 08:12 EDT 2022. Contains 354096 sequences. (Running on oeis4.)