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A309563
Cyclic permutations of length n that avoid the patterns 123 and 231.
0
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
1,5
LINKS
Miklos Bona, Michael Cory, Cyclic Permutations Avoiding Pairs of Patterns of Length Three, arXiv:1805.05196 [math.CO], 2018
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.
EXAMPLE
a(4)=1, since the only cyclic permutation of length 4 avoiding both 123 and 231 is (4231)=4312.
CROSSREFS
Cf. A000010.
Sequence in context: A372048 A053269 A163873 * A292588 A335965 A225176
KEYWORD
nonn
AUTHOR
Miklos Bona, Aug 07 2019
STATUS
approved