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%I #25 Jun 09 2016 10:26:48
%S 1,1,2,6,24,106,470,2038,8624,35754,145902,588358,2351910,9341814,
%T 36936146,145567966,572415344,2247578314,8816986046,34570684966,
%U 135522530174,531285354214,2083180354466,8170672802686,32059325714054,125845764142006,494223989283650
%N Number of permutations of length n in the 2x2 double-chevron permutation grid class.
%C The double-chevron grid class is the monotone grid class of permutations Grid((1,1),(-1,-1)).
%H David Bevan, <a href="http://demonstrations.wolfram.com/PermutationGridClasses">Permutation Grid Classes</a>
%F O.g.f: 1/sqrt(1-4*x) - x*(1-x)/((1-2*x)*(1-3*x)).
%F a(n) = A000984(n) - A027649(n-1).
%F Conjecture: n*(n^2-6*n+11)*a(n) +(-9*n^3+56*n^2-119*n+60)*a(n-1) +2*(13*n^3-83*n^2+193*n-150)*a(n-2) -12*(2*n-5)*(n^2-4*n+6)*a(n-3) =0 . - _R. J. Mathar_, Jul 24 2012
%e a(5) = 106 because the following 14 permutations can't be gridded (and hence are in the basis of the permutation class): 12543, 13254, 14253, 15243, 15423, 25413, 31254, 35412, 41253, 51243, 51423, 52413, 53412, 54123.
%t CoefficientList[Series[1/Sqrt[1-4x]-(x(1-x))/((1-2x)(1-3x)),{x,0,30}],x] (* _Harvey P. Dale_, Jun 09 2016 *)
%K nonn
%O 0,3
%A _David Bevan_, Jun 27 2012