A278301 - OEIS

%I #26 Feb 08 2019 05:37:23

%S 1,1,2,6,23,98,434,1949,8803,39888,181201,825201,3767757,17249560,

%T 79191480,364585230,1683208515,7792546040,36174065285,168367375735,

%U 785637327745,3674914227120,17230132657815,80965662243526,381275131584373,1799105397745998

%N Number of permutations of length n in the class of juxtapositions of 321-avoiders with 21-avoiders.

%C a(n) is also the number of permutations of length n in the class of juxtapositions of 231-avoiders with 21-avoiders.

%H G. C. Greubel, <a href="/A278301/b278301.txt">Table of n, a(n) for n = 0..1000</a>

%H Robert Brignall, Jakub Sliacan, <a href="https://arxiv.org/abs/1611.05370">Juxtaposing Catalan permutation classes with monotone ones</a>, arXiv:1611.05370 [math.CO], 2016.

%H Robert Brignall, Jakub Sliacan, <a href="https://arxiv.org/abs/1902.02705">Combinatorial specifications for juxtapositions of permutation classes</a>, arXiv:1902.02705 [math.CO], 2019.

%F G.f.: (1 - (1-4*x)^(1/2) + x*(-4 + (1-4*x)^(1/2) +  ((-1+5*x)^(1/2)) / ((-1+x)^(1/2)))) / (-2*x^2).

%F a(n) ~ 5^(n+3/2) / (8*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Nov 17 2016

%e There are 23 permutations of length 4 which can be expressed as a juxtaposition of a 321-avoider and a 21-avoider. Only 4321 is not expressable this way.

%t e = ee /. Solve[ee == 1 + x/(1 - x) ee, ee][[1]];

%t c = cc /. Solve[cc == 1 + x cc^2, cc][[1]];

%t cb = ccb /. Solve[ccb == 1 + x/(1 - x) ccb^2, ccb][[2]];

%t b = bb /. Solve[bb == x^2/(1 - x) + x c bb e, bb][[1]];

%t m = mm /.

%t    Solve[mm ==

%t       x c mm cb + b e x/(1 - x) (cb - 1) + x^2/(1 - x) (cb - 1),

%t      mm][[1]];

%t f = c + c m cb/(1 - x);

%t CoefficientList[Series[f, {x, 0, 25}], x]

%t Rest[CoefficientList[Series[(1 - (1 - 4 x)^(1/2) + x (-4 + (1 - 4 x)^(1/2) + ((-1 + 5 x)^(1/2)) / ((-1 + x)^(1/2))))/ (-2 x^2), {x, 0, 33}], x]] (* _Vincenzo Librandi_, Nov 18 2016 *)

%Y The other two juxtapositions of Catalan and monotone classes are enumerated by A033321, A165538.

%K nonn

%O 0,3

%A _Jakub Sliacan_, Nov 17 2016