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
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
KEYWORD
nonn
AUTHOR
Aziza Jefferson, Mar 25 2015
STATUS
approved