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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
1, 1, 6, 6, 26, 12, 42, 6, 24, 2, 48, 2, 64, 2, 56
OFFSET
1,3
COMMENTS
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.
For each n-gon, max(s_i) is equal to the maximum value in the n-th row of A285521.
EXAMPLE
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).
.
. [2,3,1,1,4,4,2,3] [2,3,1,4,1,4,2,3] [2,3,1,4,4,1,3,2]
.
. xx x x xx
. x x x x x x
. x x x x x x
. xx x x x x
.
.----------------------------------------------------------
.
. xx x x x x
. x x x x x x
. x x x x x x
. xx x x xx
.
. [3,2,4,4,1,1,3,2] [3,2,4,1,4,1,3,2] [3,2,4,1,1,4,2,3]
CROSSREFS
Cf. A285521.
Sequence in context: A077193 A056482 A255466 * A123874 A339321 A241865
KEYWORD
nonn,more
AUTHOR
Peter Kagey, May 12 2017
STATUS
approved