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Search: id:A078476
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| A078476 |
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Time taken to get n people from one side of a bridge to the other where (a) the only flashlight must be carried when crossing; (b) only one or two people may cross at the same time; (c) a pair crosses at the speed of the slowest member; and (d) the k-th person's speed requires k seconds to cross the bridge. |
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+0
1
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| 1, 2, 6, 11, 16, 22, 28, 35, 42, 50, 58, 67, 76, 86, 96, 107, 118, 130, 142, 155, 168, 182, 196, 211, 226, 242, 258, 275, 292, 310, 328, 347, 366, 386, 406, 427, 448, 470, 492, 515, 538, 562, 586, 611, 636, 662, 688, 715, 742, 770, 798, 827, 856, 886, 916, 947
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Torsten Sillke, Crossing the bridge.
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FORMULA
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For n>1: a(n)=n^2/4+3n-5+((-1)^n-1)/8.
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EXAMPLE
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a(5)=16 since one of the fastest ways is for 1&2 to cross (time 2), 1 to return (1), 4&5 to cross (5), 2 to return (2), 1&3 to cross (3), 1 to return (1) and 1&2 to cross (2) for a total time of 2+1+5+2+3+1+2=16.
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CROSSREFS
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Sequence in context: A057244 A035487 A020966 this_sequence A099056 A046691 A098167
Adjacent sequences: A078473 A078474 A078475 this_sequence A078477 A078478 A078479
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jan 03 2003
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