OFFSET
1,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv:1309.0832 [math.CO], (2013)
FORMULA
G.f.: -(24*x^6 - 71*x^5 + 84*x^4 - 45*x^3 + 11*x^2 + sqrt(-4*x + 1)*(4*x^6 - 25*x^5 + 40*x^4 - 29*x^3 + 9*x^2 - x) - x)/(8*x^6 - 54*x^5 + 117*x^4 - 114*x^3 + 54*x^2 - sqrt(-4*x + 1)*(12*x^5 - 43*x^4 + 58*x^3 - 36*x^2 + 10*x - 1) - 12*x + 1).
a(n) ~ 2^(2*n-1)/9 * (1+2/(sqrt(Pi*n))). - Vaclav Kotesovec, Mar 20 2014
Conjecture: -(n+1)*(39961*n-2474598)*a(n) +(-39961*n^2-25975201*n+4949196) *a(n-1) +3*(1460811*n^2+27429105*n-41310802) *a(n-2) +3 *(-8653921*n^2-4750029*n+74360724) *a(n-3) +4*(15005713*n^2-82481258*n+83094771) *a(n-4) +12*(-4937548*n^2+40726604*n-73155719) *a(n-5) +16*(652718*n-2110173)*(2*n-13) *a(n-6)=0. - R. J. Mathar, Jun 14 2016
EXAMPLE
Example: a(4)=12 because there are 12 sum indecomposable permutations of length 4 which avoid the patterns 3124 and 4312.
MATHEMATICA
CoefficientList[Series[- (1/x) (24 x^6 - 71 x^5 + 84 x^4 - 45 x^3 + 11 x^2 + Sqrt[-4 x + 1] (4 x^6 - 25 x^5 + 40 x^4 - 29 x^3 + 9 x^2 - x) - x) / (8 x^6 - 54 x^5 + 117 x^4 - 114 x^3 + 54 x^2 - Sqrt[-4 x + 1] (12 x^5 - 43 x^4 + 58 x^3 - 36 x^2 + 10 x - 1) - 12 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 09 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jay Pantone, Sep 08 2013
STATUS
approved