cp's OEIS Frontend

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.

%I A367873 #16 Dec 21 2023 21:12:10
%S A367873 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,
%T A367873 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,
%U A367873 43,0,0,0,0,0,0,0,106
%N 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.
%C A367873  An ascent in a permutation a(1)a(2)...a(n) is position i such that a(i) < a(i+1).
%H A367873 Tian Han and Sergey Kitaev, <a href="https://arxiv.org/abs/2311.02974">Joint distributions of statistics over permutations avoiding two patterns of length 3</a>, arXiv:2311.02974 [math.CO], 2023.
%F A367873 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.
%e A367873 1,
%e A367873 1, 1,
%e A367873 0, 4,
%e A367873 0, 4, 3,
%e A367873 0, 0, 11,
%e A367873 0, 0, 9, 7,
%e A367873 0, 0, 0, 22,
%e A367873 0, 0, 0, 16, 13,
%e A367873 0, 0, 0, 0, 37,
%e A367873 0, 0, 0, 0, 25, 21,
%e A367873 0, 0, 0, 0, 0, 56,
%e A367873 0, 0, 0, 0, 0, 36, 31,
%e A367873 0, 0, 0, 0, 0, 0, 79,
%e A367873 0, 0, 0, 0, 0, 0, 49, 43,
%e A367873 0, 0, 0, 0, 0, 0, 0, 106
%Y A367873 Cf. A367631.
%K A367873 nonn,tabf
%O A367873 0,5
%A A367873 _Tian Han_, Dec 03 2023