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A111279
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Number of permutations avoiding the patterns {3241,3421,4321}; number of weak sorting class based on 3241.
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1
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1, 2, 6, 21, 79, 309, 1237, 5026, 20626, 85242, 354080, 1476368, 6173634, 25873744, 108628550, 456710589, 1922354351, 8098984433, 34147706833, 144068881455, 608151037123, 2568318694867, 10850577045131, 45856273670841
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Is this the same sequence as A026737? - Andrew Plewe, May 09 2007
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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
| O.g.f.: (3-13*x+2*x^2+(5*x-1)*sqrt(1-4*x))/(2*(1-4*x-x^2)).
a(n) is the sum of top row terms of M^(n-1), M = an infinite square production matrix with powers of 2 as the left border as follows:
1, 1, 0, 0, 0,...
2, 1, 1, 0, 0,...
4, 1, 1, 1, 0,...
8, 1, 1, 1, 1,...
... - Gary W. Adamson, Nov 14 2011.
The top rows of these powered matrics, 1; 1,1; 3,2,1; 11,6,3,1; 43,21,10,4,1; appear also as columns in A026736. - R. J. Mathar, Nov 15 2011
Conjecture: n*a(n) +(16-13*n)*a(n-1)+(55*n-134)*a(n-2) +264-71*n)*a(n-3) +10*(7-2*n)*a(n-4) = 0. - R. J. Mathar, Nov 15 2011
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EXAMPLE
| a(4) = 21 since the top row terms of M^3 = (11, 6, 3, 1, 0, 0, 0,...)
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MATHEMATICA
| Rest[ CoefficientList[ Series[(3 - 13x + 2x^2 + (5x - 1)*Sqrt[1 - 4x])/(2*(1 - 4x - x^2)), {x, 0, 24}], x]] (* Robert G. Wilson v *)
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CROSSREFS
| Sequence in context: A150196 A148491 A026737 * A150197 A150198 A033321
Adjacent sequences: A111276 A111277 A111278 * A111280 A111281 A111282
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KEYWORD
| nonn
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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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