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Search: id:A095236
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| A095236 |
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Given a row of n pay-phones, all initially unused, how many ways are there for n people to choose the pay-phones, assuming each always chooses one of the most distant pay-phones from those in use already?. |
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+0
8
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| 1, 2, 4, 8, 16, 36, 136, 216, 672, 2592, 10656, 35904, 167808, 426240, 1866240, 15287040, 35573760, 147640320, 1323970560, 3104317440, 64865525760, 352235520000, 1891946004480, 11505792614400
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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More precisely: The first person chooses any pay-phone. 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 2L-1 and its "middle" is the outermost phone. If a span has even length, either middle may be chosen.
Each person continues to use his pay-phone until all are in use.
The problem was originally stated in terms of urinals in a mens-room.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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From 6 pay-phones: 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.
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CROSSREFS
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Cf. A095239, A095240, A095923.
Sequence in context: A034342 A034343 A002876 this_sequence A018536 A162428 A028497
Adjacent sequences: A095233 A095234 A095235 this_sequence A095237 A095238 A095239
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Jul 03 2004
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Jul 04 2004
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