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A373783
Number of ways that people can sit in n linearly arranged seats such that there are two or three empty seats between any two persons, zero, one or two empty seats at the start and end, and at least one person gets seated.
0
1, 2, 3, 4, 7, 10, 16, 30, 50, 84, 168, 312, 558, 1152, 2328, 4440, 9384, 20160, 40920, 88560, 198840, 426960, 948960, 2202480, 4965120, 11360160, 27084960, 63624960, 149995440, 366186240, 890588160, 2162401920, 5397154560, 13520183040, 33764895360, 86089651200
OFFSET
1,2
COMMENTS
The seatings are maximal in the sense that no additional person can be seated without breaking the condition in name.
FORMULA
Conjecture: a(n) = (-7*a(n-1) - 7*a(n-2) + (n-2)*a(n-3) + 3*(n+1)*a(n-4) + 4*(n-1)*a(n-5) + 3*(n-3)*a(n-6) + (n-4)*a(n-7))/3 for n >= 9. - Pontus von Brömssen, Jun 23 2024
EXAMPLE
a(5)=7 since the seating arrangements in this case (where _ denotes an empty seat) are:
1 _ _ 2 _
1 _ _ _ 2
_ 1 _ _ 2
_ _ 1 _ _
2 _ _ 1 _
2 _ _ _ 1
_ 2 _ _ 1.
Notice the number of people seated is not always the same.
CROSSREFS
Cf. A373182.
Sequence in context: A235648 A051449 A018143 * A281839 A136570 A082766
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Jun 22 2024
EXTENSIONS
More terms from Pontus von Brömssen, Jun 23 2024
STATUS
approved