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
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 (2,1,-4,1,2,-1).
FORMULA
G.f.: -(x^5-2*x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).
EXAMPLE
For n=4 the a(4) = 6 permutations are 1234, 1342, 1423, 2314, 3124, 3412.
MATHEMATICA
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 1, 1, 3, 6, 13}, 50] (* _Harvey P. Dale_, Aug 14 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
_Juan B. Gil_, Mar 10 2023
STATUS
approved