OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
David Bevan, The permutation classes Av(1234, 2341) and Av(1243, 2314), arXiv:1407.0570 [math.CO], 2014.
Kremer, Darla and Shiu, Wai Chee; Finite transition matrices for permutations avoiding pairs of length four patterns. Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
FORMULA
G.f.: F = F(z) has minimal polynomial (z-3*z^2+2*z^3) - (1-5*z+8*z^2-5*z^3)*F + (2*z-5*z^2+4*z^3)*F^2 + z^3*F^3. - David Bevan, Jun 23 2014
EXAMPLE
There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
MATHEMATICA
terms = 25;
F[_] = 0; Do[F[z_] = (z(1 - 3z + 2z^2 + z^2 F[z]^3 + (2 - 5z + 4z^2) F[z]^2 )) / (1 - 5z + 8z^2 - 5z^3) + O[z]^(terms+1), {terms+1}];
CoefficientList[F[z], z] // Rest (* Jean-François Alcover, Nov 25 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vincent Vatter, Sep 21 2009
EXTENSIONS
More terms from David Bevan, Feb 11 2014
STATUS
approved