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Search: id:A079102
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| A079102 |
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a(2n) = 2^n, a(2n+1) = 2^(2n). |
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+0
5
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| 1, 2, 4, 4, 16, 8, 64, 16, 256, 32, 1024, 64, 4096, 128, 16384, 256, 65536, 512, 262144, 1024, 1048576, 2048, 4194304, 4096, 16777216, 8192, 67108864, 16384, 268435456, 32768, 1073741824, 65536, 4294967296, 131072, 17179869184, 262144
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The number of permutations of length n containing the minimum number of monotone subsequences of length 3.
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LINKS
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Joseph Myers, The minimum number of monotone subsequences, Electronic J. Combin. 9(2) (2002), #R4.
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FORMULA
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G.f. x(8x^3+2x^2-2x-1)/(2x^2-1)/(4x^2-1). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 25 2003
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EXAMPLE
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The permutations of {0,1,2,3,4} containing the minimum number of monotone subsequences of length 3 are 10432, 13042, 13402, 14032, 20413, 20431, 21043, 21403, 23041, 23401, 24013, 24031, 30412, 31042, 31402, 34012, so a(5) = 16. Those of {0,1,2,3,4,5} are 210543, 215043, 240513, 245013, 310542, 315042, 340512, 345012, so a(6) = 8.
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CROSSREFS
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Cf. A079103, A079104, A079105, A079106.
Sequence in context: A077815 A064449 A117291 this_sequence A071337 A087481 A038210
Adjacent sequences: A079099 A079100 A079101 this_sequence A079103 A079104 A079105
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KEYWORD
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easy,nonn
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AUTHOR
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Joseph Myers (jsm(AT)polyomino.org.uk), Dec 23 2002
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