

A095236


Given a row of n payphones (or phone booths), all initially unused, how many ways are there for n people to choose the payphones, assuming each always chooses one of the most distant payphones from those in use already?.


13



1, 2, 4, 8, 16, 36, 136, 216, 672, 2592, 10656, 35904, 167808, 426240, 1866240, 15287040, 35573760, 147640320, 1323970560, 3104317440, 64865525760, 352235520000, 1891946004480, 11505792614400
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OFFSET

1,2


COMMENTS

More precisely: The first person chooses any payphone. Thereafter, each person chooses the middle of a largest span of unused phones; but a span of length L at the end of the row is taken to have length 2L1 and its "middle" is the outermost phone. If a span has even length, either middle may be chosen.
Each person continues to use his payphone until all are in use.
The problem was originally stated in terms of urinals in a mensroom.


LINKS

Table of n, a(n) for n=1..24.


EXAMPLE

From 6 payphones: A may pick any of the 6; he picks #4. B must pick #1. C must pick #6, since the others all are adjacent to A or B. D may pick #2 or #3; he picks #2. E may pick #3 or #5; he picks #5. F must pick #3. That gives the permutation (4,1,6,2,5,3), one of 36 possible permutations.


CROSSREFS

Cf. A095239, A095240, A095923, A037256.
Sequence in context: A180414 A034343 A002876 * A018536 A162428 A028497
Adjacent sequences: A095233 A095234 A095235 * A095237 A095238 A095239


KEYWORD

nonn


AUTHOR

Leroy Quet, Jul 03 2004


EXTENSIONS

Edited by Don Reble, Jul 04 2004


STATUS

approved



