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A284714 Number of indecomposable permutations avoiding the pattern 2314. 1
1, 1, 3, 13, 65, 350, 1979, 11612, 70214, 435404, 2758687, 17805613, 116784864, 776782656, 5230553221, 35604141425, 244694941741, 1696164931858, 11847948347019, 83333289416728, 589804591345417, 4198208564712140, 30037925496641695, 215941709087373510 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

A. L. L. Gao, S. Kitaev, P. B. Zhang. On pattern avoiding indecomposable permutations, arXiv:1605.05490 [math.CO], 2016.

FORMULA

G.f.: (1/2)*(sqrt(1-4*x) + 1) * (32*x/(1 + 20*x - 8*x^2 - (1-8*x)^(3/2)) - 1) [Gao, Kitaev and Zhang]. - Vaclav Kotesovec, Apr 02 2017

a(n) ~ (2+sqrt(2)) * 2^(3*n+4) / (243*sqrt(Pi)*n^(5/2)). - Vaclav Kotesovec, Apr 02 2017

MATHEMATICA

Rest[CoefficientList[Series[1/2*(Sqrt[1 - 4*x] + 1)*(32*x/(1 + 20*x - 8*x^2 - (1 - 8*x)^(3/2)) - 1), {x, 0, 20}], x]] (* Vaclav Kotesovec, Apr 02 2017 *)

PROG

(MAGMA) m:=30; R<x>:=LaurentSeriesRing(RationalField(), m); Coefficients(R!(((1/2*(Sqrt(1-4*x)+1)*(32*x/(1+20*x-8*x^2- (1-8*x)^(3/2))-1))))); // Vincenzo Librandi, Apr 04 2017

(PARI) x='x+O('x^50); Vec((1/2)*(sqrt(1-4*x) + 1) * (32*x/(1 + 20*x - 8*x^2 - (1-8*x)^(3/2)) - 1)) \\ G. C. Greubel, Apr 11 2017

CROSSREFS

Sequence in context: A126149 A060927 A074537 * A200475 A106227 A256332

Adjacent sequences:  A284711 A284712 A284713 * A284715 A284716 A284717

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 02 2017

EXTENSIONS

More terms from Vaclav Kotesovec, Apr 02 2017

STATUS

approved

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Last modified April 3 04:21 EDT 2020. Contains 333195 sequences. (Running on oeis4.)