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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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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 29 2009]
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REFERENCES
| M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb. 12 (2005)
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FORMULA
| a(n) = 3*a(n-1)-2*a(n-2)+2*a(n-3).
G.f.: 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
| 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
| Sequence in context: A174016 A129952 A057711 * A018021 A074405 A068786
Adjacent sequences: A111278 A111279 A111280 * A111282 A111283 A111284
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KEYWORD
| nonn,easy
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AUTHOR
| Len Smiley ( smiley (at) math.uaa.alaska.edu ), Nov 01 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 04 2005
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