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A361276 Number of 2413-avoiding even Grassmannian permutations of size n.

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%I A361276 #8 Aug 14 2023 12:54:34
%S A361276 1,1,1,3,6,13,22,37,55,81,111,151,196,253,316,393,477,577,685,811,946,
%T A361276 1101,1266,1453,1651,1873,2107,2367,2640,2941,3256,3601,3961,4353,
%U A361276 4761,5203,5662,6157,6670,7221,7791,8401,9031,9703,10396,11133,11892,12697,13525,14401
%N A361276 Number of 2413-avoiding even Grassmannian permutations of size n.
%C A361276 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 A361276 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 A361276 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A361276 G.f.: -(x^5-2*x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).
%e A361276 For n=4 the a(4) = 6 permutations are 1234, 1342, 1423, 2314, 3124, 3412.
%t A361276 LinearRecurrence[{2,1,-4,1,2,-1},{1,1,1,3,6,13},50] (* _Harvey P. Dale_, Aug 14 2023 *)
%Y A361276 Cf. A356185, A361272, A361273, A361274, A361275.
%Y A361276 For the corresponding odd permutations, cf. A006918.
%K A361276 nonn,easy
%O A361276 0,4
%A A361276 _Juan B. Gil_, Mar 10 2023