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.
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 (0,4,0,-6,0,4,0,-1).
FORMULA
G.f.: x^2*(2*x^4+x^2+2*x+1)/((1+x)^4*(1-x)^4).
EXAMPLE
For n=4 the a(4)=5 permutations are 1243, 2134, 2341, 2413, 4123.
PROG
(PARI) Vec(x^2*(2*x^4+x^2+2*x+1)/((1+x)^4*(1-x)^4)+O(x^50)) \\ _Michel Marcus_, Mar 07 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
_Juan B. Gil_, Mar 07 2023
STATUS
approved