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A116699
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Number of permutations of length n which avoid the patterns 123 and 4312.
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5
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1, 2, 5, 13, 30, 61, 112, 190, 303, 460, 671, 947, 1300, 1743, 2290, 2956, 3757, 4710, 5833, 7145, 8666, 10417, 12420, 14698, 17275, 20176, 23427, 27055, 31088, 35555, 40486, 45912, 51865, 58378, 65485, 73221, 81622, 90725, 100568, 111190, 122631, 134932
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also number of permutations of length n which avoid the patterns 123, 2314, 4312; or avoid the patterns 321, 1243, 3421, etc.
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LINKS
| Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
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FORMULA
| G.f.: A(x) = {x(2x^3-5x^2+3x-1)}/{(x-1)^5}
a(n) = (n^4 + 2n^3 - 13n^2 + 34n)/24. - Franklin T. Adams-Watters, Sep 16 2006
Partial sums of A105163. - Levi R. Self (levi.r.self(AT)gmail.com), Aug 04 2007
Binomial transform of [1, 1, 2, 3, 1, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007
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MATHEMATICA
| LinearRecurrence[{5, -10, 10, -5, 1}, {1, 2, 5, 13, 30}, 50] (* From Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
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PROG
| (PARI) for(n=1, 100, print1((n^4 + 2*n^3 - 13*n^2 + 34*n)/24", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 22 2008
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CROSSREFS
| Sequence in context: A178444 A122025 A057873 * A054127 A184052 A018012
Adjacent sequences: A116696 A116697 A116698 * A116700 A116701 A116702
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Feb 26 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Mar 16 2008
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 22 2008
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