A326348 Number of permutations of length n in the class of juxtapositions of separable permutations with 21-avoiders.

1, 1, 2, 6, 24, 115, 609, 3409, 19728, 116692, 701062, 4261581, 26146111, 161631115, 1005522262, 6289410686, 39525228204, 249427451071, 1579885391573, 10040587733693, 64004713573508, 409139527503760, 2622049900367018, 16843666877986873, 108438876033442579

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Robert Brignall, Jakub Sliacan, Combinatorial specifications for juxtapositions of permutation classes, arXiv:1902.02705 [math.CO], 2019.

Formula

G.f.: (2-4*z+z^2)*x*y/(4*(1-z)*(-2+7*z-7*z^2+z^3)) + ((-2+10*z-15*z^2+7*z^3)*x + (2-6*z+z^2+6*z^3-z^4)*y - 10+54*z-99*z^2+66*z^3-9z^4)/(4*(1-z)^2*(-2+7*z-7*z^2+z^3)) where x=sqrt(1-6*z+z^2) and y=sqrt(1-8*z+8z^2).

Example

There are a(5) = 115 permutations of length 5 which can be expressed as a juxtaposition of a separable permutation (avoiding 2413 and 3142) with an increasing permutation. These 5 cannot be expressed: 25143, 35142, 35241, 41532 and 42531.

Crossrefs

Other juxtapositions of algebraic classes with monotone ones are enumerated by A033321, A165538, and A278301.

Sequence in context: A216717 A174072 A224255 * A128088 A069657 A369766

Adjacent sequences: A326345 A326346 A326347 * A326349 A326350 A326351

Keyword

nonn

Author

Robert Brignall, Sep 11 2019

Status

approved