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.

1, 1, 2, 2, 8, 16, 24, 48, 192, 1536, 4608, 18432, 23040, 92160, 241920, 1935360, 3870720, 41287680, 371589120, 11890851840, 29727129600, 237817036800, 1248539443200, 19976631091200, 11236854988800, 42807066624000, 176579149824000, 3390319676620800, 6886586843136000

Offset: 1

Author

Max Alekseyev, Apr 10 2023

Keywords

• nonn

Comments

Provides the same counts as A095239, but up to a choice for the first payphone.

Links

• Max Alekseyev, Table of n, a(n) for n = 1..100
• Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.

Crossrefs

Cf. A095236, A095239, A095240, A095912, A358056, A361295, A361296, A362192.

Formula

a(n) = A095239(n) / n = A095240(n+1) / 2.