A228769 The number of skew sum decomposable permutations which avoid the patterns 3124 and 4312.

0, 1, 3, 10, 35, 129, 494, 1935, 7670, 30582, 122280, 489552, 1960956, 7855994, 31471731, 126063782, 504888839, 2021777865, 8094784697, 32405289263, 129709206465, 519129580361, 2077477804103, 8313000733125, 33261722967167, 133076495664483, 532391828669675, 2129796460981743, 8519701993370619, 34079469569317323

Offset: 1

Author

Jay Pantone, Sep 08 2013

Keywords

• nonn

Examples

			Example: a(4)=10 because there are 10 skew sum decomposable permutations of length 4 which avoid the patterns 3124 and 4312.
		

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)

Crossrefs

The class of all permutations which avoid the patterns 3124 and 4312 is given by A165534.

Programs

Mathematica

CoefficientList[Series[- (1/x) (3 x^4 - x^3 + Sqrt[-4 x + 1] (4 x^5 - 9 x^4 + 9 x^3 - 2 x^2)) / (12 x^4 - 31 x^3 + 27 x^2 + Sqrt[-4 x + 1] (4 x^4 - 13 x^3 + 15 x^2 - 7 x + 1) - 9 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 09 2013 *)

Formula

G.f.: -(3*x^4 - x^3 + sqrt(-4*x + 1)*(4*x^5 - 9*x^4 + 9*x^3 - 2*x^2))/(12*x^4 - 31*x^3 + 27*x^2 + sqrt(-4*x + 1)*(4*x^4 - 13*x^3 + 15*x^2 - 7*x + 1) - 9*x + 1).

a(n) ~ 4^(n-1)/9 * (1 + 1/sqrt(Pi*n)). - Vaclav Kotesovec, Mar 18 2014