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Search: id:A116721
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| A116721 |
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Number of permutations of length n which avoid the patterns 123, 3142, 4312; or avoid the patterns 123, 3421, 4231. |
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+0
1
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| 1, 2, 5, 12, 24, 42, 67, 100, 142, 194, 257, 332, 420, 522, 639, 772, 922, 1090, 1277, 1484, 1712, 1962, 2235, 2532, 2854, 3202, 3577, 3980, 4412, 4874, 5367, 5892, 6450, 7042, 7669, 8332, 9032, 9770, 10547, 11364, 12222, 13122, 14065, 15052, 16084
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
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FORMULA
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G.f.: A(x) = -{x(x^4-3x^2+2x-1)}/{(x-1)^4}
For n >= 2, a(n) = (n^3 + 3n^2 - 16n + 24)/6. - Franklin T. Adams-Watters, Sep 16 2006
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MAPLE
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A116721 := proc(n) coeftayl(-x*(x^4-3*x^2+2*x-1)/(x-1)^4, x=0, n) ; end: seq(A116721(n), n=1..60) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2008
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CROSSREFS
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Sequence in context: A112287 A127787 A116733 this_sequence A116713 A116714 A023615
Adjacent sequences: A116718 A116719 A116720 this_sequence A116722 A116723 A116724
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KEYWORD
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nonn,easy
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AUTHOR
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Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Feb 26 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2008
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