A361271 Number of 1342-avoiding odd Grassmannian permutations of size n.

0, 0, 1, 2, 6, 9, 19, 25, 44, 54, 85, 100, 146, 167, 231, 259, 344, 380, 489, 534, 670, 725, 891, 957, 1156, 1234, 1469, 1560, 1834, 1939, 2255, 2375, 2736, 2872, 3281, 3434, 3894, 4065, 4579, 4769, 5340, 5550, 6181, 6412, 7106, 7359, 8119, 8395, 9224, 9524, 10425

Offset

0,4

Comments

A permutation is said to be Grassmannian if it has at most one descent. A permutation is odd if it has an odd number of inversions.

a(n) is also the number of 3124-avoiding odd Grassmannian permutations of size n.

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

Formula

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

Example

For n=4 the a(4)=6 permutations are 1243, 1324, 2134, 2341, 2413, 4123.

Prog

(PARI) seq(n) = Vec(x^2*(x^4+x^2+x+1)/((1+x)^3*(1-x)^4) + O(x*x^n), -n-1) \\ Andrew Howroyd, Mar 07 2023

Crossrefs

Cf. A356185, A361270, A361274.

Sequence in context: A367464 A076738 A291100 * A082290 A325536 A182984

Adjacent sequences: A361268 A361269 A361270 * A361272 A361273 A361274

Keyword

nonn,easy

Author

Juan B. Gil, Mar 07 2023

Status

approved