cp's OEIS Frontend

A383040 Number of king permutations on n elements avoiding the mesh pattern (12, {(0,1),(0,2),(1,0),(2,0)}).

%I A383040 #25 Apr 25 2025 15:11:41
%S A383040 1,1,0,0,2,12,78,568,4674,42944,436314,4860020,58914870,772330276,
%T A383040 10888803374,164310553184,2642525580218,45124440536632,
%U A383040 815438318526482,15547317496485932,311912067538692126,6568399090178800988,144867849880285518694,3339550150164041194232,80315480372245746015970
%N A383040 Number of king permutations on n elements avoiding the mesh pattern (12, {(0,1),(0,2),(1,0),(2,0)}).
%C A383040 A permutation p(1)p(2)...p(n) is a king permutation if |p(i+1)-p(i)|>1 for each 0<i<n. The sequence counts the number a(n) of king permutations of length n that avoid the mesh pattern 12 with squares (0,1), (0,2), (1,0), and (2,0) shaded.
%H A383040 Dan Li and Philip B. Zhang, <a href="https://arxiv.org/abs/2411.18131">Distributions of mesh patterns of short lengths on king permutations</a>, arXiv:2411.18131 [math.CO], 2024. See Theorem 4.1 at page 13.
%F A383040 G.f.: (1 + t)^2*A(t)/(1 + t + t*A(t)) where A(t)=Sum_{n >= 0} n!*t^n*(1-t)^n/(1+t)^n is the g.f. for king permutations given by A002464.
%e A383040 For n = 4 the a(4) = 2 solutions are the two permutations 2413 and 3142.
%e A383040 For n = 5 the a(5) = 12 solutions are these 12 permutations: 24135, 24153, 25314, 31425, 31524, 35142, 35241, 41352, 42513, 42531, 52413, 53142.
%Y A383040 Cf. A002464, A382644, A382645, A382651.
%K A383040 nonn,easy
%O A383040 0,5
%A A383040 _Dan Li_, Apr 22 2025