cp's OEIS Frontend

A361294 A variant of payphone permutations: given a circular booth with n payphones, one of which is already occupied, a(n) is the number ways for n-1 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, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones.

%I A361294 #14 Apr 16 2023 20:54:45
%S A361294 1,1,2,2,8,16,24,48,192,1536,4608,18432,23040,92160,241920,1935360,
%T A361294 3870720,41287680,371589120,11890851840,29727129600,237817036800,
%U A361294 1248539443200,19976631091200,11236854988800,42807066624000,176579149824000,3390319676620800,6886586843136000
%N A361294 A variant of payphone permutations: given a circular booth with n payphones, one of which is already occupied, a(n) is the number ways for n-1 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, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones.
%C A361294 Provides the same counts as A095239, but up to a choice for the first payphone.
%H A361294 Max Alekseyev, <a href="/A361294/b361294.txt">Table of n, a(n) for n = 1..100</a>
%H A361294 Max A. Alekseyev, <a href="https://arxiv.org/abs/2304.04324">Enumeration of Payphone Permutations</a>, arXiv:2304.04324 [math.CO], 2023.
%F A361294 a(n) = A095239(n) / n = A095240(n+1) / 2.
%Y A361294 Cf. A095236, A095239, A095240, A095912, A358056, A361295, A361296, A362192.
%K A361294 nonn
%O A361294 1,3
%A A361294 _Max Alekseyev_, Apr 10 2023