A367873 Irregular triangle read by rows: T(n,k) = number of permutations of length n avoiding simultaneously the patterns 132 and 321 with the maximum number of non-overlapping ascents equal to k.

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

Offset: 0

Author

Tian Han, Dec 03 2023

Keywords

• nonn
• tabf

Comments

An ascent in a permutation a(1)a(2)...a(n) is position i such that a(i) < a(i+1).

Examples

			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
		

Links

• Tian Han and Sergey Kitaev, Joint distributions of statistics over permutations avoiding two patterns of length 3, arXiv:2311.02974 [math.CO], 2023.

Crossrefs

Cf. A367631.

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.