OFFSET
0,5
COMMENTS
An ascent in a permutation a(1)a(2)...a(n) is position i such that a(i) < a(i+1).
LINKS
Tian Han and Sergey Kitaev, Joint distributions of statistics over permutations avoiding two patterns of length 3, arXiv:2311.02974 [math.CO], 2023.
FORMULA
G.f.: (1 + x + x^2 - 2*x^2*y + x^3*y + x^4*y + 3*x^4*y^2 + 2*x^5*y^2)/(1 - x^2*y)^3.
EXAMPLE
1,
1, 1,
0, 4,
0, 4, 3,
0, 0, 11,
0, 0, 9, 7,
0, 0, 0, 22,
0, 0, 0, 16, 13,
0, 0, 0, 0, 37,
0, 0, 0, 0, 25, 21,
0, 0, 0, 0, 0, 56,
0, 0, 0, 0, 0, 36, 31,
0, 0, 0, 0, 0, 0, 79,
0, 0, 0, 0, 0, 0, 49, 43,
0, 0, 0, 0, 0, 0, 0, 106
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Tian Han, Dec 03 2023
STATUS
approved