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%I #20 Mar 08 2023 02:49:29
%S 0,0,1,2,5,8,16,20,38,40,75,70,131,112,210,168,316,240,453,330,625,
%T 440,836,572,1090,728,1391,910,1743,1120,2150,1360,2616,1632,3145,
%U 1938,3741,2280,4408,2660,5150,3080,5971,3542,6875,4048,7866,4600,8948,5200,10125
%N Number of 1324-avoiding odd Grassmannian permutations of size n.
%C A permutation is said to be Grassmannian if it has at most one descent. A permutation is odd if it has an odd number of inversions.
%H Juan B. Gil and Jessica A. Tomasko, <a href="https://arxiv.org/abs/2207.12617">Pattern-avoiding even and odd Grassmannian permutations</a>, arXiv:2207.12617 [math.CO], 2022.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1).
%F G.f.: x^2*(2*x^4+x^2+2*x+1)/((1+x)^4*(1-x)^4).
%e For n=4 the a(4)=5 permutations are 1243, 2134, 2341, 2413, 4123.
%o (PARI) Vec(x^2*(2*x^4+x^2+2*x+1)/((1+x)^4*(1-x)^4)+O(x^50)) \\ _Michel Marcus_, Mar 07 2023
%Y Cf. A356185, A361271.
%K nonn,easy
%O 0,4
%A _Juan B. Gil_, Mar 07 2023