%I A109033
%S A109033 1,1,2,6,22,88,368,1584,6968,31192,141656,651136,3023840,14166496,
%T A109033 66876096,317809216,1519163456,7299577216,35237444736,170812433536,
%U A109033 831127053696,4057858988416,19873611712896,97609555091456
%N A109033 Number of permutations in S_n avoiding the patterns 1342 and 2143.
%C A109033 Also number of permutations in S_n avoiding the patterns 3142 and 2341. 
               Partial sums of A109034.
%C A109033 Hankel transform is 2^floor(n^2/3) (see A134751). [From Paul Barry (pbarry(AT)wit.ie), 
               Dec 15 2008]
%D A109033 Ian Le, Wilf classes of pairs of permutations of length 4, The Electronic 
               J. of Combinatorics, 12, 2005, R25.
%F A109033 G.f.=[1-sqrt(1-8x+16x^2-8x^3)]/[4x(1-x)]
%F A109033 Contribution from Paul Barry (pbarry(AT)wit.ie), Dec 15 2008: (Start)
%F A109033 G.f.: (1-x)c(2x(1-x)^2), c(x) the g.f. of A000108;
%F A109033 a(n):=sum{k=0..n, (-1)^(n-k)*C(2k+1,n-k)*2^k*A000108(k)}; (End)
%F A109033 G.f.: 1/(1-x/(1-x/(1-2x/(1-x/(1-x/(1-2x/(1-x/(1-x/(1-2x...... (continued 
               fraction). [From Paul Barry (pbarry(AT)wit.ie), Dec 15 2008]
%F A109033 a(n)= Sum_{k, 0<=k<=n} A091866(n,k)*2^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 27 2009]
%e A109033 a(4)=22 because all permutations of 1234 qualify with the exception of 
               1342 and 2143.
%p A109033 G:=(1-sqrt(1-8*x+16*x^2-8*x^3))/4/x/(1-x): Gser:=series(G,x=0,30): 1,
               seq(coeff(Gser,x^n),n=1..27);
%Y A109033 Cf. A109034.
%Y A109033 Sequence in context: A165537 A165538 A165539 this_sequence A049135 A049127 
               A049137
%Y A109033 Adjacent sequences: A109030 A109031 A109032 this_sequence A109034 A109035 
               A109036
%K A109033 nonn,new
%O A109033 0,3
%A A109033 Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 16 2005