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A373829
Number of inefficient arrangements in A373182, where inefficient means that the maximum number of persons that a seating arrangement can hold is not achieved.
0
0, 0, 1, 0, 6, 2, 36, 24, 246, 240, 1920, 2424, 16920, 25920, 166440, 297360, 1809360, 3669840, 21551040, 48666240, 279180720, 691649280, 3908580480, 10501787520, 58813776000, 169809696000, 946627274880, 2914924320000, 16228733875200, 52963370208000
OFFSET
1,5
COMMENTS
The maximum number of persons that can be seated in the arrangements in A373182 in n seats is ceiling(n/2).
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.
The ratio a(n)/A373182(n) -> 1 as n -> infinity (at a much slower initial rate for even n).
FORMULA
a(n) = A373182(n) - (ceiling((n+1)/2))!.
EXAMPLE
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.
1 _ _ 2 _
_ 1 _ 2 _
_ 1 _ _ 2
_ 2 _ 1 _
2 _ _ 1 _
_ 2 _ _ 1.
For n=9 seats the maximum number of persons that can be seated is 5, hence examples of inefficient arrangements are:
3 _ 2 _ 1 _ _ 4 _
_ 3 _ _ 1 _ _ 2 _.
CROSSREFS
Sequence in context: A096039 A201229 A038256 * A242529 A263088 A266231
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Jun 19 2024
STATUS
approved