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

0,4

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.

Links

Table of n, a(n) for n=0..50.

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).

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

Example

For n=4 the a(4) = 5 permutations are 1234, 1342, 2314, 3124, 3412.

Maple

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

Crossrefs

Cf. A356185, A361272, A361273, A361274.

For the corresponding odd permutations, cf. A005993.

Sequence in context: A181747 A078864 A208574 * A342230 A023218 A073022

Adjacent sequences: A361272 A361273 A361274 * A361276 A361277 A361278

Keyword

nonn,easy

Author

Juan B. Gil, Mar 10 2023

Status

approved