A361275 Number of 1423-avoiding even Grassmannian permutations of size n.

1, 1, 1, 3, 5, 11, 17, 29, 41, 61, 81, 111, 141, 183, 225, 281, 337, 409, 481, 571, 661, 771, 881, 1013, 1145, 1301, 1457, 1639, 1821, 2031, 2241, 2481, 2721, 2993, 3265, 3571, 3877, 4219, 4561, 4941, 5321, 5741, 6161, 6623, 7085, 7591, 8097, 8649, 9201, 9801, 10401

Offset: 0

Author

Juan B. Gil, Mar 10 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.

Avoiding any of the patterns 2314 or 3412 gives the same sequence.

Examples

			For n=4 the a(4) = 5 permutations are 1234, 1342, 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 (2,1,-4,1,2,-1).

Crossrefs

Cf. A356185, A361272, A361273, A361274.

For the corresponding odd permutations, cf. A005993.

Programs

Maple

seq(1 - 5*n/24 + n^3/12 - (-1)^n * n/8, n = 0 .. 100); # Robert Israel, Mar 10 2023

Formula

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

a(n) = 1 - 5*n/24 + n^3/12 - (-1)^n * n/8. - Robert Israel, Mar 10 2023