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A variant of payphone permutations: given a circular booth with n payphones, a(n) is the number ways for n people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible.
6

%I #7 Apr 16 2023 20:55:15

%S 1,2,6,8,60,144,336,384,8640,57600,221760,967680,4193280,9031680,

%T 14515200,30965760,2368880640,50164531200,582465945600,7357464576000,

%U 50214695731200,245494068019200,1443672502272000,24103053950976000,200858782924800000,835572536967168000

%N A variant of payphone permutations: given a circular booth with n payphones, a(n) is the number ways for n people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible.

%H Max Alekseyev, <a href="/A361296/b361296.txt">Table of n, a(n) for n = 1..100</a>

%H Max A. Alekseyev, <a href="https://arxiv.org/abs/2304.04324">Enumeration of Payphone Permutations</a>, arXiv:2304.04324 [math.CO], 2023.

%Y Cf. A095236, A095239, A095912, A358056, A361294, A361295, A362192.

%K nonn

%O 1,2

%A _Max Alekseyev_, Apr 08 2023