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 A256336 Number of Largest Chain Ladder Family (LCLF) matchings on n edges. 0
 1, 3, 14, 81, 521, 3554, 25172, 183129, 1359863, 10264359, 78521474, 607449380, 4744167924, 37355679904, 296232263792, 2363773540473, 18965408058723, 152910824717297, 1238260516988018, 10066874219853977, 82134185988563049, 672294915226393926, 5519252917557226452 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Largest Chain Ladder Family (LCLF) of matchings is the largest family of matchings formed by repeated edge inflations by ladders and vertex insertions into a chain of any length. REFERENCES A. Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, Ph. D. Dissertation, Univ. of Florida, Math., 2015. LINKS FORMULA G.f. f satisfies 2x^3f^6-2x^2f^5+4x^2f^4-3xf^3+2xf^2+f-1=0. EXAMPLE a(3)=14 because of the 15 matchings on 3 edges, only one does not lie in the Largest Chain Ladder Family. In canonical sequence form, the missing matching is given by 123123. MAPLE f := RootOf(2*x^3*_Z^6-2*x^2*_Z^5+4*x^2*_Z^4-3*x*_Z^3+2*x*_Z^2+_Z-1, 1); series(f, x=0, 30); CROSSREFS Sequence in context: A000264 A009053 A202474 * A256338 A256331 A292875 Adjacent sequences:  A256333 A256334 A256335 * A256337 A256338 A256339 KEYWORD nonn AUTHOR Aziza Jefferson, Mar 25 2015 STATUS approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)