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

Author

Juan B. Gil, Mar 09 2023

Keywords

• nonn
• easy

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.

Examples

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

Links

• 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).

Crossrefs

Cf. A175287, A356185, A361273.

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