

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
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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

Table of n, a(n) for n=1..23.


FORMULA

G.f. f satisfies 2x^3f^62x^2f^5+4x^2f^43xf^3+2xf^2+f1=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^62*x^2*_Z^5+4*x^2*_Z^43*x*_Z^3+2*x*_Z^2+_Z1, 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



