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.
Avoiding any of the patterns 2314 or 3412 gives the same sequence.
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-x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).
a(n) = 1 - 5*n/24 + n^3/12 - (-1)^n * n/8. - _Robert Israel_, Mar 10 2023
EXAMPLE
For n=4 the a(4) = 5 permutations are 1234, 1342, 2314, 3124, 3412.
MAPLE
seq(1 - 5*n/24 + n^3/12 - (-1)^n * n/8, n = 0 .. 100); # _Robert Israel_, Mar 10 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
_Juan B. Gil_, Mar 10 2023
STATUS
approved