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

1,3

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.

Formula

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

Crossrefs

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

Sequence in context: A248097 A098273 A342835 * A220172 A276054 A192305

Adjacent sequences: A361291 A361292 A361293 * A361295 A361296 A361297

Keyword

nonn

Author

Max Alekseyev, Apr 10 2023

Status

approved