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A111281
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Number of permutations avoiding the patterns {2413,2431,4213,3412,3421,4231,4321,4312}; number of strong sorting class based on 2413.
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1
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1, 1, 2, 6, 16, 40, 100, 252, 636, 1604, 4044, 10196, 25708, 64820, 163436, 412084, 1039020, 2619764, 6605420, 16654772, 41993004, 105880308, 266964460, 673118772, 1697188012, 4279255412, 10789627756, 27204748468, 68593500716, 172950260724, 436073277676
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OFFSET
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0,3
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COMMENTS
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a(n) = term (1,1) in M^n, M = the 4x4 matrix [1,1,1,1; 0,1,0,1; 0,0,1,1; 1,0,0,1]. - Gary W. Adamson, Apr 29 2009
Number of permutations of length n>0 avoiding the partially ordered pattern (POP) {1>2, 1>4} of length 4. That is, number of length n permutations having no subsequences of length 4 in which the first element is larger than the second and fourth elements. - Sergey Kitaev, Dec 09 2020
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LINKS
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M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb. 12 (2005) R31.
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FORMULA
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a(n) = 3*a(n-1)-2*a(n-2)+2*a(n-3).
G.f.: 1+x*(1-x+2*x^2)/(1-3*x+2*x^2-2*x^3). - Colin Barker, Jan 16 2012
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MATHEMATICA
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a[1] = 1; a[2] = 2; a[3] = 6; a[n_] := a[n] = 3a[n - 1] - 2a[n - 2] + 2a[n - 3]; Table[a[n], {n, 28}] (* Robert G. Wilson v *)
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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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