A361273 Number of 1324-avoiding even Grassmannian permutations of size n.

1, 1, 1, 3, 6, 13, 20, 37, 47, 81, 91, 151, 156, 253, 246, 393, 365, 577, 517, 811, 706, 1101, 936, 1453, 1211, 1873, 1535, 2367, 1912, 2941, 2346, 3601, 2841, 4353, 3401, 5203, 4030, 6157, 4732, 7221, 5511, 8401, 6371, 9703, 7316, 11133, 8350, 12697, 9477, 14401, 10701

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..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 (0,4,0,-6,0,4,0,-1).

Formula

G.f.: -(x^7+2*x^6-7*x^5-8*x^4+x^3+3*x^2-x-1)/((x+1)^4*(x-1)^4).

Example

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

Crossrefs

Cf. A356185, A361270, A361272.

Sequence in context: A230370 A285246 A147009 * A318228 A064290 A064621

Adjacent sequences: A361270 A361271 A361272 * A361274 A361275 A361276

Keyword

nonn,easy

Author

Juan B. Gil, Mar 09 2023

Status

approved