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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. 2
 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; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 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.: (1-4*x+4*x^2-4*x^3-(1-2*x)*sqrt(1-4*x))/(2*x*(1-x)^2*sqrt(1-4*x)). a(n) = n(C(n) - C(n-1) - ... - C(1)), where C(n) denotes the n-th Catalan number. a(n) ~ 2^(2*n+1)/(3*sqrt(Pi*n)). - Vaclav Kotesovec, Mar 20 2014 EXAMPLE a(5)=100 because 100 permutations of length 5 have at least one cyclic rotation which avoids 132. MATHEMATICA Rest[CoefficientList[Series[(1-4*x+4*x^2-4*x^3-(1-2*x)*Sqrt[1-4*x]) / (2*x*(1-x)^2*Sqrt[1-4*x]), {x, 0, 20}], x]] (* Vaclav Kotesovec, Mar 20 2014 *) PROG (PARI) x='x+O('x^50); Vec((1-4*x+4*x^2-4*x^3-(1-2*x)*sqrt(1-4*x))/(2*x*(1-x)^2*sqrt(1-4*x))) \\ G. C. Greubel, Mar 21 2017 CROSSREFS Cf. A141254. Sequence in context: A060725 A150299 A094012 * A306672 A324063 A078486 Adjacent sequences:  A141250 A141251 A141252 * A141254 A141255 A141256 KEYWORD nonn AUTHOR Vincent Vatter, Jun 17 2008 STATUS approved

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Last modified June 22 12:56 EDT 2021. Contains 345380 sequences. (Running on oeis4.)