OFFSET
0,5
COMMENTS
a(n) is zero when n choose 2 is odd, that is for numbers that have remainders 2 or 3 when divided by 4.
LINKS
Gal Beniamini, Nir Lavee, and Nati Linial, How Balanced Can Permutations Be?, arXiv:2306.16954 [math.CO], 2023. See p. 18.
Tanya Khovanova, 3-Symmetric Permutations
Wikipedia, Inversion
FORMULA
EXAMPLE
Consider a permutation 1432. It has exactly three pairs of numbers, the first of them is 1, that are in increasing order. The other three pairs are in decreasing order. The other 5 permutations of size 4 with this property are 2341, 2413, 3142, 3214, 4123. Thus a(4) = 6.
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Oct 22 2018
EXTENSIONS
a(10)-a(15) from Giovanni Resta, Oct 22 2018
a(16)-a(28) from Alois P. Heinz, Oct 24 2018
STATUS
approved