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%I #13 Jun 22 2024 16:11:43
%S 0,0,1,0,6,2,36,24,246,240,1920,2424,16920,25920,166440,297360,
%T 1809360,3669840,21551040,48666240,279180720,691649280,3908580480,
%U 10501787520,58813776000,169809696000,946627274880,2914924320000,16228733875200,52963370208000
%N Number of inefficient arrangements in A373182, where inefficient means that the maximum number of persons that a seating arrangement can hold is not achieved.
%C The maximum number of persons that can be seated in the arrangements in A373182 in n seats is ceiling(n/2).
%C The seatings here are maximal in the sense that no additional person can be seated without breaking the condition in A373182, but maximum seatings are excluded.
%C The ratio a(n)/A373182(n) -> 1 as n -> infinity (at a much slower initial rate for even n).
%F a(n) = A373182(n) - (ceiling((n+1)/2))!.
%e a(5)=6 are the following seatings, where _ denotes an empty seat. Seatings of 3 people are the maximum for n=5 and those are not included.
%e 1 _ _ 2 _
%e _ 1 _ 2 _
%e _ 1 _ _ 2
%e _ 2 _ 1 _
%e 2 _ _ 1 _
%e _ 2 _ _ 1.
%e For n=9 seats the maximum number of persons that can be seated is 5, hence examples of inefficient arrangements are:
%e 3 _ 2 _ 1 _ _ 4 _
%e _ 3 _ _ 1 _ _ 2 _.
%Y Cf. A081123, A373182.
%K nonn
%O 1,5
%A _Enrique Navarrete_, Jun 19 2024
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