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A284714 Number of indecomposable permutations avoiding the pattern 2314. 1

%I #21 Sep 08 2022 08:46:19

%S 1,1,3,13,65,350,1979,11612,70214,435404,2758687,17805613,116784864,

%T 776782656,5230553221,35604141425,244694941741,1696164931858,

%U 11847948347019,83333289416728,589804591345417,4198208564712140,30037925496641695,215941709087373510

%N Number of indecomposable permutations avoiding the pattern 2314.

%H Vincenzo Librandi, <a href="/A284714/b284714.txt">Table of n, a(n) for n = 1..1000</a>

%H A. L. L. Gao, S. Kitaev, P. B. Zhang. <a href="https://arxiv.org/abs/1605.05490">On pattern avoiding indecomposable permutations</a>, arXiv:1605.05490 [math.CO], 2016.

%F 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

%F a(n) ~ (2+sqrt(2)) * 2^(3*n+4) / (243*sqrt(Pi)*n^(5/2)). - _Vaclav Kotesovec_, Apr 02 2017

%t 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 *)

%o (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

%o (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

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Apr 02 2017

%E More terms from _Vaclav Kotesovec_, Apr 02 2017

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)