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Search: id:A141253
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| A141253 |
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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. |
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2
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| 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
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OFFSET
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1,2
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REFERENCES
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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.
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FORMULA
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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 nth Catalan number.
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EXAMPLE
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a(5)=100 because 100 permutations of length 5 have at least one cyclic rotation which avoids 132.
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CROSSREFS
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Cf. A141254.
Adjacent sequences: A141250 A141251 A141252 this_sequence A141254 A141255 A141256
Sequence in context: A053504 A060725 A094012 this_sequence A078486 A129817 A128652
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KEYWORD
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nonn
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AUTHOR
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Vince Vatter (vince(AT)mcs.st-and.ac.uk), Jun 17 2008
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