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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.
6
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 A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.
FORMULA
a(n) = A095239(n) / n = A095240(n+1) / 2.
KEYWORD
nonn
AUTHOR
Max Alekseyev, Apr 10 2023
STATUS
approved