# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a308726
Showing 1-1 of 1

%I A308726 #33 Oct 29 2021 07:40:23
%S A308726 1,1,2,6,24,112,556,2811,14234,71808,360568,1803100,8988924,44719588,
%T A308726 222221416,1103827306,5484124128,27265300504,135695994964,
%U A308726 676228846370,3374996253420,16871826671280,84488005896720,423828619074900,2129868537725916,10722045181336524
%N A308726 The number of permutations of length n and tier at most 1, that is, the number of permutations of length n sortable by two passes through a stack where outputting the longest prefix matching the identity permutation is prioritized.
%C A308726 This counts the permutations of length n that avoid the permutations 24153, 24513, 24531, 34251, 35241, 42513, 42531, 45231, 261453, 231564, 523164.
%D A308726 Toufik Mansour, Howard Skogman, and Rebecca Smith. "Passing through a stack k times." Discrete Mathematics, Algorithms and Applications 11.01 (2019): 1950003.
%H A308726 Toufik Mansour, Howard Skogman, and Rebecca Smith, <a href="https://arxiv.org/abs/1704.04288">Passing through a stack k times</a>, arXiv:1704.04288 [math.CO], 2017-2018.
%F A308726 G.f.: (2 + (2*x-1)/sqrt(1-4*x) - sqrt(2*sqrt(1-4*x) - 1)) / (2*x). - _Vaclav Kotesovec_, Jun 30 2019
%F A308726 a(n) ~ 2^(4*n + 3/2) / (sqrt(Pi) * n^(3/2) * 3^(n + 1/2)). - _Vaclav Kotesovec_, Jun 30 2019
%F A308726 Conjecture: D-finite with recurrence: 3*n*(n-1)*(n+1)*a(n) -n*(n-1)*(67*n-101)*a(n-1) +2*(n-1)*(286*n^2-1112*n+1089)*a(n-2) +4*(-580*n^3+4200*n^2-10106*n+8049)*a(n-3) +24*(184*n^3-1784*n^2+5770*n-6221)*a(n-4) -96*(4*n-15)*(2*n-9)*(4*n-17)*a(n-5)=0. - _R. J. Mathar_, Jan 27 2020
%t A308726 CoefficientList[Series[(2 + (2*x - 1)/Sqrt[1 - 4*x] - Sqrt[2*Sqrt[1 - 4*x] - 1])/(2*x), {x, 0, 25}], x] (* _Vaclav Kotesovec_, Jun 30 2019 *)
%Y A308726 Cf. A122890 (sum of last two rows), A158830 (sum of first two rows).
%K A308726 nonn
%O A308726 0,3
%A A308726 _Rebecca Smith_, Jun 20 2019
%E A308726 More terms from _Vaclav Kotesovec_, Jun 30 2019

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE