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A165540
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Number of permutations of length n which avoid the patterns 1234 and 2341.
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1
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1, 2, 6, 22, 89, 376, 1611, 6901, 29375, 123996, 518971, 2155145, 8888348, 36442184, 148669894, 603984658, 2445184835, 9870338447, 39746337616, 159728191141, 640811439917, 2567220813272, 10272592695691, 41064215020977, 164014588869574, 654627778362521, 2611244306191009, 10410752330836178, 41488934932279847, 165282459721996836, 658248561748273483
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OFFSET
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1,2
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COMMENTS
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These permutations have an enumeration scheme of depth 6.
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LINKS
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FORMULA
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G.f.: ((2-10*z+9*z^2+7*z^3-4*z^4)*sqrt(1-4*z) - (2-16*z+41*z^2-39*z^3+12*z^4)) / ((1-4*z)*(1-3*z+z^2)*((1-z)*sqrt(1-4*z) + (1-3*z))). - David Bevan, Jun 23 2014
Conjecture: +(14681*n+187954)*(n+3) *a(n) +(14681*n^2-2696783*n-4897218) *a(n-1) +(-888761*n^2+12771539*n+5490342) *a(n-2) +2*(1635223*n^2-14850835*n+13281012) *a(n-3) +2*(-1908503*n^2+15402653*n-25889820) *a(n-4) +156*(2*n-7)*(3301*n-14374) *a(n-5)=0. - R. J. Mathar, Jun 14 2016
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EXAMPLE
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There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
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MATHEMATICA
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Rest[CoefficientList[ Series[ ((2-10z+9z^2+7z^3-4z^4) Sqrt[1-4z] -(2-16z+41z^2-39z^3+12z^4)) / ((1-4z) (1-3z+z^2) ((1-z) Sqrt[1-4z] +(1-3z))), {z, 0, 40}], z]] (* David Bevan, Jun 23 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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