%I A088921
%S A088921 1,2,5,13,33,80,185,411,885,1862,3853,7881,15993,32284,64945,130359,
%T A088921 261293,523282,1047397,2095781,4192721,8386792,16775145,33552083,
%U A088921 67106213,134214750,268432125,536867201,1073737705,2147479092
%N A088921 The number of 321- 2143-avoiding permutations of length n.
%C A088921 321- 2143-avoiding permutations of length n are in one-to-one correspondence 
               with simple Dyck paths of semilength n (a Dyck path is simple if 
               it has at most one long upward edge or at most one long downward 
               edge, an edge being "long" if it consists of at least two steps). 
               They are the Grassmannian permutations and their inverses. They can 
               also be characterized as those permutations whose essential set is 
               contained in one row or one column. This sequence also enumerates 
               the cyclic arrangements of 1, 2, ... n+1 which avoid the cyclic arrangement 
               1234.
%C A088921 Also, number of 1324-avoiding circular permutations on [n+1].
%D A088921 S. Billey, W. Jockusch and R.P. Stanley. Some combinatorial properties 
               of Schubert polynomials, Journal of Algebraic Combinatorics 2(4):345-374, 
               1993
%D A088921 K. Eriksson and S. Linusson. Combinatorics of Fulton's essential set. 
               Duke Mathematical Journal 85(1):61-76, 1996.
%D A088921 A. Vella. Pattern avoidance in permutations: linear and cyclic orders, 
               Electron. J. Combin. 9 (2002/03), no. 2, Research paper 18, 43 pp.
%H A088921 D. Callan, <a href="http://arXiv.org/abs/math.CO/0210014">Pattern avoidance 
               in circular permutations</a>.
%F A088921 2^(i+1) - binomial(i+1, 3) - 2i - 1
%F A088921 G.f.= x(2x^4-5x^3+7x^2-4x+1)/[(1-2x)(1-x)^4]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Feb 22 2004
%Y A088921 Cf. A000325.
%Y A088921 Sequence in context: A108890 A027929 A001659 this_sequence A005183 A005348 
               A067676
%Y A088921 Adjacent sequences: A088918 A088919 A088920 this_sequence A088922 A088923 
               A088924
%K A088921 easy,nonn
%O A088921 1,2
%A A088921 Antoine Vella (avella(AT)math.uwaterloo.ca), Oct 23 2003