A309563 Cyclic permutations of length n that avoid the patterns 123 and 231.

1, 1, 1, 1, 2, 3, 2, 2, 4, 6, 2, 2, 6, 8, 4, 4, 6, 10, 4, 4, 10, 12, 4, 4, 12, 18, 6, 6, 8, 12, 8, 8, 16, 22, 6, 6, 18, 22, 8, 8, 12, 22, 10, 10, 22, 26, 8, 8, 20, 32, 12, 12, 18, 24, 12, 12, 28, 36, 8, 8, 30, 38, 16, 16, 20, 36, 16, 16, 24, 30, 12, 12, 36, 54

Offset: 1

Author

Miklos Bona, Aug 07 2019

Keywords

• nonn

Examples

			a(4)=1, since the only cyclic permutation of length 4 avoiding both 123 and 231 is (4231)=4312.
		

Links

• Miklos Bona, Michael Cory, Cyclic Permutations Avoiding Pairs of Patterns of Length Three, arXiv:1805.05196 [math.CO], 2018

Crossrefs

Cf. A000010.

Formula

a(2)=1; a(n)=phi(n/2) if n=4k, a(n)=phi((n+2)/4) +phi(n/2) if n=4k+2 > 2, and a(n)=phi((n+1)/2) if n is odd, where phi is the Euler totient function.