A141254 Number of permutations that lie in the cyclic closure of Av(123) - i.e., at least one cyclic rotation of the permutation avoids the pattern 123.

1, 1, 2, 6, 24, 110, 510, 2268, 9632, 39492, 158190, 624745, 2447808, 9552244, 37214086, 144932760, 564676096, 2201735552, 8592780798, 33568042425, 131261440720, 513747571680, 2012524130518, 7890178181831, 30957296889264

Offset

0,3

Links

Table of n, a(n) for n=0..24.

M. D. Atkinson, M. H. Albert, R. E. L. Aldred, H. P. van Ditmarsch, C. C. Handley, D. A. Holton, D. J. McCaughan, C. Monteith, Cyclically closed pattern classes of permutations, Australasian J. Combinatorics 38 (2007), 87-100.

Formula

a(n) = n * (C(n) - 2^n + binomial(n,2) + 2) for n >= 4.

Example

a(5)=110 because 110 permutations of length 5 have at least one cyclic rotation which avoids 123.

Crossrefs

Cf. A141253.

Sequence in context: A230695 A177519 A214762 * A366706 A216879 A372527

Adjacent sequences: A141251 A141252 A141253 * A141255 A141256 A141257

Keyword

nonn

Author

Vincent Vatter, Jun 17 2008

Status

approved