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A141253 Number of permutations that lie in the cyclic closure of Av(132) - i.e. at least one cyclic rotation of the permutation avoids the pattern 132. 1
1, 2, 6, 24, 100, 408, 1631, 6440, 25263, 98790, 385803, 1506156, 5881057, 22974406, 89804910, 351279584, 1375035208, 5386203792, 21113167346, 82816267480, 325055630634, 1276635121388, 5016837177052, 19725798613152, 77601159558800 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

REFERENCES

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.

R. Brignall, S. Huczynska, V. Vatter, Simple permutations and algebraic generating functions, J. Combinatorial Theory, Series A 115 (2008), 423-441.

FORMULA

g.f. = (1-4x+4x^2-4x^3-(1-2x)sqrt(1-4x)) / (2x(1-x)^2sqrt(1-4x)). a(n) = n(C(n) - C(n-1) - ... - C(1)), where C(n) denotes the n-th Catalan number.

EXAMPLE

a(5)=100 because 100 permutations of length 5 have at least one cyclic rotation which avoids 132.

CROSSREFS

Cf. A141254.

Sequence in context: A060725 A150299 A094012 * A078486 A129817 A128652

Adjacent sequences:  A141250 A141251 A141252 * A141254 A141255 A141256

KEYWORD

nonn

AUTHOR

Vince Vatter (vince(AT)mcs.st-and.ac.uk), Jun 17 2008

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Last modified February 13 03:07 EST 2012. Contains 205435 sequences.