A361274 Number of 1342-avoiding even Grassmannian permutations of size n.

1, 1, 1, 3, 5, 12, 17, 32, 41, 67, 81, 121, 141, 198, 225, 302, 337, 437, 481, 607, 661, 816, 881, 1068, 1145, 1367, 1457, 1717, 1821, 2122, 2241, 2586, 2721, 3113, 3265, 3707, 3877, 4372, 4561, 5112, 5321, 5931, 6161, 6833, 7085, 7822, 8097, 8902, 9201, 10077, 10401

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.

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

Examples

			For n=4 the a(4) = 5 permutations are 1234, 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 (1,3,-3,-3,3,1,-1).

Crossrefs

Cf. A356185, A361271.

Programs

Mathematica

LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,1,1,3,5,12,17},51] (* Stefano Spezia, Mar 09 2023 *)

Formula

G.f.: -(2*x^6-x^5-5*x^4-2*x^3+3*x^2-1)/((x+1)^3*(x-1)^4).

E.g.f.: ((24 - 9*x + 6*x^2 + 2*x^3)*cosh(x) + (33 - 6*x + 9*x^2 + 2*x^3)*sinh(x))/24. - Stefano Spezia, Mar 09 2023