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%I #17 Apr 12 2023 11:18:15
%S 1,2,4,6,12,28,104,152,528,2208,9120,23616,130944,278784,1635840,
%T 14181120,32186880,116674560,1262039040,2443714560,58920099840,
%U 161981890560,1416311930880,7700720025600,120779469619200
%N Variant of the pay-phone sequence A095236. Here a slot at the end of the row is always preferred over a slot sandwiched immediately between two used slots.
%H Max Alekseyev, <a href="/A095912/b095912.txt">Table of n, a(n) for n = 1..100</a>
%H Max A. Alekseyev, <a href="https://arxiv.org/abs/2304.04324">Enumeration of Payphone Permutations</a>, arXiv:2304.04324 [math.CO], 2023.
%H Simon Wundling, <a href="https://arxiv.org/abs/2303.18175">About a combinatorial problem with n seats and n people</a>, arXiv:2303.18175 [math.CO], 2023. (German)
%e Example: there are 5 payphones. First arrival may choose any; he selects phone #2. Next arrival must take the furthest away, #5. Next arrival must take either of #3 or #4 (since both have a neighbor on one side and a vacant slot on the other); he chooses #3. Next arrival must take #1 (because end slots are preferred over "sandwiched" slots), leaving #4 for the last arrival. The permutation (25314) is one of a(5)=10 that satisfy the requirements.
%Y Cf. A095236, A095239, A095240, A095923.
%K nonn
%O 1,2
%A _Jon Wild_, Jul 13 2004
%E Corrected and extended by _Don Reble_, Jul 15 2004
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