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
Paolo Xausa, Table of n, a(n) for n = 0..10000
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.
MATHEMATICA
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 1, 1, 3, 6, 12}, 60] (* Paolo Xausa, Mar 02 2026 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Juan B. Gil, Mar 09 2023
STATUS
approved