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

1,3

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.: -(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

Example

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

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 *)

Crossrefs

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

Sequence in context: A128736 A303730 A149037 * A361768 A296164 A151046

Adjacent sequences: A228766 A228767 A228768 * A228770 A228771 A228772

Keyword

nonn

Author

Jay Pantone, Sep 08 2013

Status

approved