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A228769 The number of skew sum decomposable permutations which avoid the patterns 3124 and 4312. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A296164 A151046 A221130

Adjacent sequences:  A228766 A228767 A228768 * A228770 A228771 A228772

KEYWORD

nonn

AUTHOR

Jay Pantone, Sep 08 2013

STATUS

approved

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Last modified November 18 07:22 EST 2019. Contains 329252 sequences. (Running on oeis4.)