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A116731
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Number of permutations of length n which avoid the patterns 321, 2143, 3124; or avoid the patterns 132, 2314, 4312, etc.
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5
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1, 2, 5, 12, 25, 46, 77, 120, 177, 250, 341, 452, 585, 742, 925, 1136, 1377, 1650, 1957, 2300, 2681, 3102, 3565, 4072, 4625, 5226, 5877, 6580, 7337, 8150, 9021, 9952, 10945, 12002, 13125, 14316, 15577, 16910, 18317, 19800, 21361, 23002, 24725, 26532
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Conjecture: also counts the distinct pairs (flips, iterations) that a bubble sort program generates when sorting all permutations of 1..n. [From Wouter Meeussen (wouter.meeussen(AT)pandora.be), Dec 13 2008]
A006527+1=A116731 (* From Vladimir Joseph Stephan Orlovsky, May 04 2011 *)
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
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FORMULA
| G.f.: A(x) = {(3x^2-2x+1)x}/{(x-1)^4}
a(n) = (n^3-3*n^2+5*n)/3. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 13 2006
Row sums of triangle A130154. Also, binomial transform of [1, 1, 2, 2, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007
Binomial transform of [1, 1, 2, 2, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007
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MATHEMATICA
| Table[(n^3-3*n^2+5*n)/3, {n, 100}] (* From Vladimir Joseph Stephan Orlovsky, May 04 2011 *)
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CROSSREFS
| Cf. A006527,A130154.
Sequence in context: A096584 A002836 A116720 * A116722 A116730 A067331
Adjacent sequences: A116728 A116729 A116730 * A116732 A116733 A116734
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KEYWORD
| nonn,easy
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AUTHOR
| Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Feb 26 2006
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EXTENSIONS
| More terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 13 2006
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