A284714 Number of indecomposable permutations avoiding the pattern 2314.

1, 1, 3, 13, 65, 350, 1979, 11612, 70214, 435404, 2758687, 17805613, 116784864, 776782656, 5230553221, 35604141425, 244694941741, 1696164931858, 11847948347019, 83333289416728, 589804591345417, 4198208564712140, 30037925496641695, 215941709087373510

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 A352705

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