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A228771
The number of skew sum indecomposable permutations which avoid the patterns 3124 and 4312.
1
1, 1, 3, 12, 53, 234, 1013, 4306, 18051, 74903, 308487, 1263393, 5152139, 20941298, 84897207, 343467388, 1387244237, 5595368133, 22543241377, 90739796783, 364954106877, 1466865660103, 5892463315373, 23658818086719, 94952826295865, 380947979933041, 1527871081396065, 6126157580638517, 24557525359295337, 98421154766829972
OFFSET
1,3
LINKS
Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv:1309.0832 [math.CO], (2013)
FORMULA
G.f.: (8*x^6 - 28*x^5 + 50*x^4 - 35*x^3 + 10*x^2 - sqrt(-4*x + 1)*(6*x^5 - 18*x^4 + 21*x^3 - 8*x^2 + x) - x)/(8*x^5 - 46*x^4 + 71*x^3 - 43*x^2 - sqrt(-4*x + 1)*(12*x^4 - 31*x^3 + 27*x^2 - 9*x + 1) + 11*x - 1).
a(n) ~ 4^(n-1)/3 * (1+1/sqrt(Pi*n)). - Vaclav Kotesovec, Mar 20 2014
Conjecture: -163*(n+2)*(4*n-413) *a(n) +(-652*n^2-725425*n-452889) *a(n-1) +5*(14473*n^2+512276*n-443094) *a(n-2) +(-410045*n^2-2408964*n+8429009) *a(n-3) +2*(404156*n^2-1297075*n-1518084)*a(n-4) -8*(29333*n-32490)*(2*n-11)*a(n-5)=0. - R. J. Mathar, Jun 14 2016
EXAMPLE
Example: a(4)=12 because there are 12 skew sum indecomposable permutations of length 4 which avoid the patterns 3124 and 4312.
MATHEMATICA
CoefficientList[Series[(1/x) (8 x^6 - 28 x^5 + 50 x^4 - 35 x^3 + 10 x^2 - Sqrt[-4 x + 1] (6 x^5 - 18 x^4 + 21 x^3 - 8 x^2 + x) - x) / (8 x^5 - 46 x^4 + 71 x^3 - 43 x^2 - Sqrt[-4 x + 1] (12 x^4 - 31 x^3 + 27 x^2 - 9 x + 1) + 11 x - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 09 2013 *)
CROSSREFS
A228771(n) = A165534(n) - A228769(n)
Sequence in context: A299113 A124202 A138269 * A370023 A151198 A151199
KEYWORD
nonn
AUTHOR
Jay Pantone, Sep 08 2013
EXTENSIONS
Corrected a(17) by Vincenzo Librandi, Sep 09 2013
STATUS
approved