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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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7
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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
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OFFSET
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1,2
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COMMENTS
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Row sums of triangle A130154. Also, binomial transform of [1, 1, 2, 2, 0, 0, 0, ...]. - Gary W. Adamson, Oct 23 2007
Conjecture: also counts the distinct pairs (flips, iterations) that a bubble sort program generates when sorting all permutations of 1..n. - Wouter Meeussen, Dec 13 2008
a(n) is the number of lattice points (x,y) in the closed region bounded by the parabolas y = x*(x - n) and y = x*(n - x). - Clark Kimberling, Jun 01 2013
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LINKS
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FORMULA
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G.f.: (3*x^2 - 2*x + 1)*x/(x - 1)^4.
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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