A282847 - OEIS

%I #27 Aug 12 2022 09:17:43

%S 0,0,0,1,3,4,4,6,8,10,12,14,17,20

%N Given n people seated at a table, a(n) is the minimum number of swaps that must occur in order for everybody to have sat next to every other person.

%C a(n) >= ceiling(n(n-3)/8).

%H Mathematics Stack Exchange, <a href="http://math.stackexchange.com/questions/833541">Making Friends around a Circular Table</a>

%e For n = 7 the a(7) = 4 swaps are:

%e (1) 1 swaps with 4,

%e (2) 1 swaps with 5,

%e (3) 3 swaps with 6, and then

%e (4) 2 swaps with 6.

%K nonn,hard,more

%O 1,5

%A _Peter Kagey_, Feb 24 2017

%E a(13) and a(14) added by _Dmitry Kamenetsky_, Feb 26 2017