cp's OEIS Frontend

A363785 A variant of payphone permutations: given a row of 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, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones.

%I A363785 #8 Jun 22 2023 06:05:40
%S A363785 1,2,4,6,16,28,120,264,576,2784,11040,37440,204672,679680,2511360,
%T A363785 15655680,52945920,232796160,2456801280,11867627520,97875025920,
%U A363785 576737280000,4012233523200,20013325516800,215802239385600,1778700504268800,9687506721177600,88613303353344000,448250987623219200
%N A363785 A variant of payphone permutations: given a row of 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, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones.
%H A363785 Max Alekseyev, <a href="/A363785/b363785.txt">Table of n, a(n) for n = 1..100</a>
%H A363785 Max A. Alekseyev, <a href="https://arxiv.org/abs/2304.04324">Enumeration of Payphone Permutations</a>, arXiv:2304.04324 [math.CO], 2023.
%Y A363785 Cf. A358056, A095236, A095239, A095912, A361294, A361295, A361296, A362192, A363785.
%K A363785 nonn
%O A363785 1,2
%A A363785 _Max Alekseyev_, Jun 21 2023