OFFSET
1,2
COMMENTS
The Largest Hairpin Family of matchings is the largest family of matchings formed by repeated edge inflations and vertex insertions into the single edge and the hairpin.
LINKS
Aziza Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, PhD Thesis, University of Florida, 2015.
FORMULA
G.f. f satisfies x*f^3 - (2*x+2)*f^2 + 5*f - 3 = 0.
EXAMPLE
a(3) = 14 because of the 15 matchings on 3 edges, only 1 does not lie in the Largest Hairpin Family. In canonical sequence form, the missing matching is given by 121323.
MAPLE
f := RootOf(_Z^3*x-2*_Z^2*x-2*_Z^2+5*_Z-3, 1);
series(f, x=0, 30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Aziza Jefferson, Mar 25 2015
STATUS
approved