A256336 Number of Largest Chain Ladder Family (LCLF) matchings on n edges.

1, 3, 14, 81, 521, 3554, 25172, 183129, 1359863, 10264359, 78521474, 607449380, 4744167924, 37355679904, 296232263792, 2363773540473, 18965408058723, 152910824717297, 1238260516988018, 10066874219853977, 82134185988563049, 672294915226393926, 5519252917557226452

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.

Links

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

Aziza Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, PhD Thesis, University of Florida, 2015.

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: A347001 A354325 A346966 * A256338 A256331 A292875

Adjacent sequences: A256333 A256334 A256335 * A256337 A256338 A256339

Keyword

nonn

Author

Aziza Jefferson, Mar 25 2015

Status

approved