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 3124-avoiding even Grassmannian permutations of size n.
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 (1,3,-3,-3,3,1,-1).
FORMULA
G.f.: -(2*x^6-x^5-5*x^4-2*x^3+3*x^2-1)/((x+1)^3*(x-1)^4).
E.g.f.: ((24 - 9*x + 6*x^2 + 2*x^3)*cosh(x) + (33 - 6*x + 9*x^2 + 2*x^3)*sinh(x))/24. - _Stefano Spezia_, Mar 09 2023
EXAMPLE
For n=4 the a(4) = 5 permutations are 1234, 1423, 2314, 3124, 3412.
MATHEMATICA
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 1, 1, 3, 5, 12, 17}, 51] (* _Stefano Spezia_, Mar 09 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
_Juan B. Gil_, Mar 09 2023
STATUS
approved