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A143017
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Number of {2-1-3, 2'^e-31}-avoiding permutations of size n (see definition in the Elizalde paper).
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0
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1, 2, 4, 9, 22, 56, 147, 396, 1088, 3036, 8582, 24524, 70727, 205594, 601756, 1771937, 5245544, 15602496, 46606356, 139753120, 420520000, 1269361000, 3842722454, 11663928644, 35490451807, 108232655126, 330760284892
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| S. Elizalde, Generating trees for permutations avoiding generalized patterns, Annals of Combinatorics 11 (2007), 435-458; arXiv:0707.4633.
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FORMULA
| a(n)=(1/n)Sum[2*binom(n,2k)*binom(n-k,k-1)+n*binom(n,2k+1)*binom(n-k,k)/(n-k) G.f. G(x) satisfies xG^3 +(4x-2)G^2 +(4x-1)G + x = 0.
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MAPLE
| a:=proc(n) options operator, arrow: (sum(2*binomial(n, 2*k)*binomial(n-k, k-1)+n*binomial(n, 2*k+1)*binomial(n-k, k)/(n-k), k=0..floor((1/2)*n)))/n end proc: seq(a(n), n=1..27);
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CROSSREFS
| Sequence in context: A091561 A025265 A037245 * A130018 A099754 A105633
Adjacent sequences: A143014 A143015 A143016 * A143018 A143019 A143020
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 17 2008
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