A361273 Number of 1324-avoiding even Grassmannian permutations of size n.

1, 1, 1, 3, 6, 13, 20, 37, 47, 81, 91, 151, 156, 253, 246, 393, 365, 577, 517, 811, 706, 1101, 936, 1453, 1211, 1873, 1535, 2367, 1912, 2941, 2346, 3601, 2841, 4353, 3401, 5203, 4030, 6157, 4732, 7221, 5511, 8401, 6371, 9703, 7316, 11133, 8350, 12697, 9477, 14401, 10701

Offset: 0

Author

Juan B. Gil, Mar 09 2023

Keywords

• nonn
• easy

Comments

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.

Examples

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

Links

• Juan B. Gil and Jessica A. Tomasko, Pattern-avoiding even and odd Grassmannian permutations, arXiv:2207.12617 [math.CO], 2022.
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Crossrefs

Cf. A356185, A361270, A361272.

Formula

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).