A346660 - OEIS

%I #20 Nov 09 2021 04:33:54

%S 1,1,1,2,5,14,42,133,442,1537,5583,21165,83707,345324,1485687,6663354,

%T 31134078,151408319,765462514,4017644518,21860398111,123120413119,

%U 716701884408,4305828784896,26661920519485,169937265101628,1113616036893636,7494786443901137

%N Number of cyclic patterns of length n that avoid the vincular pattern 23-1-4.

%C The vincular pattern 23-1-4 requires the 2 and the 3 to be adjacent.

%C By the trivial Wilf equivalence obtained by reversing the permutations, a(n) is also the number of cyclic patterns of length n that avoid the vincular pattern 32-4-1.

%H Vaclav Kotesovec, <a href="/A346660/b346660.txt">Table of n, a(n) for n = 0..500</a>

%H Rupert Li, <a href="https://arxiv.org/abs/2107.12353">Vincular Pattern Avoidance on Cyclic Permutations</a>, arXiv:2107.12353 [math.CO], 2021.

%F For n >= 2, a(n) = Sum_{i=0..n-2} binomial(n-2,i) * A092920(i).

%Y Cf. A025242, A047970, A092920, A346661.

%K nonn

%O 0,4

%A _Rupert Li_, Aug 03 2021