A361276 Number of 2413-avoiding even Grassmannian permutations of size n.

1, 1, 1, 3, 6, 13, 22, 37, 55, 81, 111, 151, 196, 253, 316, 393, 477, 577, 685, 811, 946, 1101, 1266, 1453, 1651, 1873, 2107, 2367, 2640, 2941, 3256, 3601, 3961, 4353, 4761, 5203, 5662, 6157, 6670, 7221, 7791, 8401, 9031, 9703, 10396, 11133, 11892, 12697, 13525, 14401

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.

Links

Table of n, a(n) for n=0..49.

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

Example

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

Mathematica

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 1, 1, 3, 6, 13}, 50] (* Harvey P. Dale, Aug 14 2023 *)

Crossrefs

Cf. A356185, A361272, A361273, A361274, A361275.

For the corresponding odd permutations, cf. A006918.

Sequence in context: A019079 A280029 A178097 * A211870 A239987 A048134

Adjacent sequences: A361273 A361274 A361275 * A361277 A361278 A361279

Keyword

nonn,easy

Author

Juan B. Gil, Mar 10 2023

Status

approved