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

Author

Aziza Jefferson, Mar 25 2015

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Programs

Maple

f := RootOf(_Z^3*x-2*_Z^2*x-2*_Z^2+5*_Z-3, 1);
series(f, x=0, 30);

Formula

G.f. f satisfies x*f^3 - (2*x+2)*f^2 + 5*f - 3 = 0.