A361271 Number of 1342-avoiding odd Grassmannian permutations of size n.

0, 0, 1, 2, 6, 9, 19, 25, 44, 54, 85, 100, 146, 167, 231, 259, 344, 380, 489, 534, 670, 725, 891, 957, 1156, 1234, 1469, 1560, 1834, 1939, 2255, 2375, 2736, 2872, 3281, 3434, 3894, 4065, 4579, 4769, 5340, 5550, 6181, 6412, 7106, 7359, 8119, 8395, 9224, 9524, 10425

Offset: 0

Author

Juan B. Gil, Mar 07 2023

Keywords

• nonn
• easy

Comments

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.

a(n) is also the number of 3124-avoiding odd Grassmannian permutations of size n.

Examples

			For n=4 the a(4)=6 permutations are 1243, 1324, 2134, 2341, 2413, 4123.
		

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 (1,3,-3,-3,3,1,-1).

Crossrefs

Cf. A356185, A361270, A361274.

Programs

PARI

seq(n) = Vec(x^2*(x^4+x^2+x+1)/((1+x)^3*(1-x)^4) + O(x*x^n), -n-1) \\ Andrew Howroyd, Mar 07 2023

Formula

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