cp's OEIS Frontend

A118888 Number of ways to place n objects with weights 1,2,...,n evenly spaced around the circumference of a circular disk such that the remaining imbalance is minimized.

%I A118888 #16 Oct 25 2019 05:02:48
%S A118888 1,1,1,1,1,2,1,2,3,24,1,732,1,720,48,144,2
%N A118888 Number of ways to place n objects with weights 1,2,...,n evenly spaced around the circumference of a circular disk such that the remaining imbalance is minimized.
%C A118888 The position of weight 1 is kept fixed at position 1. Mirror configurations are counted only once. For n not a prime power, the sequence equals A118887.
%H A118888 G. J. Woeginger, <a href="http://dx.doi.org/10.4169/amer.math.monthly.120.09.849">Nothing new about equiangular polygons</a>, Amer. Math. Monthly, 120 (2013), 849-850.
%e A118888 a(5)=1: The configuration minimizing the remaining imbalance with respect to the center of the circle is [1 4 3 2 5] (and its mirror image).
%e A118888 Examples of minimum imbalance configurations not in A118887:
%e A118888 a(7)=1: [1 4 7 2 3 5 6];
%e A118888 a(8)=2: [1 4 7 3 6 2 5 8], [1 7 4 3 6 5 2 8];
%e A118888 a(9)=3: [1 5 9 2 7 3 4 8 6], [1 5 9 4 2 6 7 3 8], [1 6 5 4 9 2 3 7 8];
%e A118888 a(11)=1: [1 8 9 5 2 6 10 7 3 4 11];
%e A118888 a(13)=1: [1 2 7 12 13 4 5 3 8 6 11 9 10];
%e A118888 a(16)=144: lexicographically earliest [1 3 5 13 16 7 10 2 14 4 6 9 12 8 11 15];
%e A118888 a(17)=2: [1 7 3 17 10 9 15 2 14 6 5 4 16 8 13 12 11],
%e A118888 [1 8 9 3 16 4 12 13 14 2 10 5 6 7 17 11 15] and their mirror configurations (e.g. [1 11 12 13 8 ...]) both produce a center of gravity with distance 2.1884*10^(-7) from the center of a circle with radius 1. All other configurations produce greater distances, e.g. [1 3 11 16 9 5 7 12 14 4 10 8 2 15 13 6 17] -> 2.5126*10^(-7). - _Hugo Pfoertner_, Oct 24 2019
%Y A118888 Cf. A118887, A326921.
%K A118888 hard,more,nonn
%O A118888 1,6
%A A118888 _Hugo Pfoertner_, May 26 2006
%E A118888 a(17) corrected by _Hugo Pfoertner_, Oct 24 2019