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A361275
Number of 1423-avoiding even Grassmannian permutations of size n.
1
1, 1, 1, 3, 5, 11, 17, 29, 41, 61, 81, 111, 141, 183, 225, 281, 337, 409, 481, 571, 661, 771, 881, 1013, 1145, 1301, 1457, 1639, 1821, 2031, 2241, 2481, 2721, 2993, 3265, 3571, 3877, 4219, 4561, 4941, 5321, 5741, 6161, 6623, 7085, 7591, 8097, 8649, 9201, 9801, 10401
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.
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
For the corresponding odd permutations, cf. A005993.
Sequence in context: A181747 A078864 A208574 * A342230 A023218 A073022
KEYWORD
nonn,easy
AUTHOR
_Juan B. Gil_, Mar 10 2023
STATUS
approved