A361272 Number of 1243-avoiding even Grassmannian permutations of size n.

1, 1, 1, 3, 6, 12, 20, 32, 47, 67, 91, 121, 156, 198, 246, 302, 365, 437, 517, 607, 706, 816, 936, 1068, 1211, 1367, 1535, 1717, 1912, 2122, 2346, 2586, 2841, 3113, 3401, 3707, 4030, 4372, 4732, 5112, 5511, 5931, 6371, 6833, 7316, 7822, 8350, 8902, 9477, 10077

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.

a(n) is also the number of sigma-avoiding even Grassmannian permutations of size n, where sigma is any of the patterns 2134, 2341, or 4123.

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 (3,-2,-2,3,-1).

Formula

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

a(n) = (57 - 9*(-1)^n - 28*n + 6*n^2 + 4*n^3)/48. - Stefano Spezia, Mar 09 2023

Example

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

Crossrefs

Cf. A175287, A356185, A361273.

Sequence in context: A066140 A200067 A061061 * A001975 A096220 A034333

Adjacent sequences: A361269 A361270 A361271 * A361273 A361274 A361275

Keyword

nonn,easy

Author

Juan B. Gil, Mar 09 2023

Status

approved