A256331 Number of Largest Hairpin Family matchings on n edges.

1, 3, 14, 81, 527, 3684, 27022, 205149, 1598303, 12705939, 102653652, 840419676, 6956988612, 58132229976, 489673597926, 4153635860373, 35449185841679, 304179698619129, 2622657870000646, 22710277017073785, 197418128701387895

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

Table of n, a(n) for n=1..21.

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

Sequence in context: A346966 A256336 A256338 * A292875 A077054 A355291

Adjacent sequences: A256328 A256329 A256330 * A256332 A256333 A256334

Keyword

nonn

Author

Aziza Jefferson, Mar 25 2015

Status

approved