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A054394
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Number of permutations with certain forbidden subsequences.
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2
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1, 1, 2, 5, 14, 42, 132, 429, 1429, 4847, 16660, 57820, 202086, 709928, 2503266, 8850681, 31355020, 111242127, 395091069, 1404332528, 4994581900, 17771328588, 63253477326, 225194224134, 801884971816, 2855809269782, 10171707099565
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OFFSET
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0,3
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REFERENCES
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E. Barcucci et al., From Motzkin to Catalan Permutations, Discr. Math., 217 (2000), 33-49.
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LINKS
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Table of n, a(n) for n=0..26.
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FORMULA
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Conjecture: g.f.(x)=1+z*(1-2z+z^2-z^3)/(1-3z+3z^2-3z^3+2z^4-z^5) where z=x*A001006(x) and A001006(x) is the g.f. of A001006. [From R. J. Mathar, Jul 07 2009]
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CROSSREFS
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Interpolates between Motzkin numbers (A001006) and Catalan numbers (A000108). Cf. A005773, A054391-A054393.
Sequence in context: A036768 A058094 A080938 * A036769 A033191 A211216
Adjacent sequences: A054391 A054392 A054393 * A054395 A054396 A054397
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Elisa Pergola (elisa(AT)dsi.unifi.it), May 21 2000
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STATUS
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approved
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