OFFSET
1,2
LINKS
M. H. Albert, M. D. Atkinson, and V. Vatter, Inflations of geometric grid classes: three case studies, arXiv:1209.0425 [math.CO], 2012.
Christian Bean, Finding structure in permutation sets, Ph.D. Dissertation, Reykjavík University, School of Computer Science, 2018.
Darla Kremer and Wai Chee Shiu, 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 satisfies: x^3*f^6+(7*x^3-7*x^2+2*x)*f^5+(x^4+14*x^3-21*x^2+10*x-1)*f^4+(4*x^4+8*x^3-19*x^2+11*x-2)*f^3+(6*x^4-5*x^3-2*x^2+2*x)*f^2+(4*x^4-7*x^3+4*x^2-x)*f+x^4-2*x^3+x^2 = 0.
EXAMPLE
There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
MATHEMATICA
f = 0; m = 24;
Do[f = -(1/(x(4x^3 - 7x^2 + 4x - 1)))(x^3 f^6 + x(7x^2 - 7x + 2) f^5 + (x^4 + 14x^3 - 21x^2 + 10x - 1) f^4 + (1 - 2x)^2 (x^2 + 3x - 2) f^3 + x(6 x^3 - 5x^2 - 2x + 2) f^2 + (x-1)^2 x^2) + O[x]^m, {m}];
CoefficientList[f/x, x] (* Jean-François Alcover, Feb 17 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vincent Vatter, Sep 21 2009
EXTENSIONS
Reference corrected by Vincent Vatter, Sep 04 2012
STATUS
approved