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Number of 1243-avoiding even Grassmannian permutations of size n.
4

%I #21 Mar 09 2023 17:33:46

%S 1,1,1,3,6,12,20,32,47,67,91,121,156,198,246,302,365,437,517,607,706,

%T 816,936,1068,1211,1367,1535,1717,1912,2122,2346,2586,2841,3113,3401,

%U 3707,4030,4372,4732,5112,5511,5931,6371,6833,7316,7822,8350,8902,9477,10077

%N Number of 1243-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.

%C a(n) is also the number of sigma-avoiding even Grassmannian permutations of size n, where sigma is any of the patterns 2134, 2341, or 4123.

%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_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).

%F G.f.: -(2*x^4-4*x^3+2*x-1)/((x+1)*(x-1)^4).

%F a(n) = (57 - 9*(-1)^n - 28*n + 6*n^2 + 4*n^3)/48. - _Stefano Spezia_, Mar 09 2023

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

%Y Cf. A175287, A356185, A361273.

%K nonn,easy

%O 0,4

%A _Juan B. Gil_, Mar 09 2023