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Number of 1324-avoiding even Grassmannian permutations of size n.
3

%I #8 Mar 09 2023 20:02:37

%S 1,1,1,3,6,13,20,37,47,81,91,151,156,253,246,393,365,577,517,811,706,

%T 1101,936,1453,1211,1873,1535,2367,1912,2941,2346,3601,2841,4353,3401,

%U 5203,4030,6157,4732,7221,5511,8401,6371,9703,7316,11133,8350,12697,9477,14401,10701

%N Number of 1324-avoiding even Grassmannian permutations of size n.

%C A permutation is said to be Grassmannian if it has at most one descent. A permutation is even if it has an even 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^7+2*x^6-7*x^5-8*x^4+x^3+3*x^2-x-1)/((x+1)^4*(x-1)^4).

%e For n=4 the a(4) = 6 permutations are 1234, 1342, 1423, 2314, 3124, 3412.

%Y Cf. A356185, A361270, A361272.

%K nonn,easy

%O 0,4

%A _Juan B. Gil_, Mar 09 2023