A256332 Number of D&P Family matchings on n edges.

1, 3, 13, 65, 351, 1994, 11747, 71117, 439765, 2765775, 17636697, 113766694, 741032618, 4867177299, 32199559769, 214369107989, 1435126789097, 9655274425496, 65246685081291, 442668997422749, 3014127038713923, 20590331364902095, 141078438156193677, 969270926188235574, 6676082724399618966, 46089922748156948822, 318876966533117953114, 2210580887889464667057, 15353093117180070481879, 106816339860746421126519

Offset: 1

Author

Aziza Jefferson, Mar 25 2015

Keywords

• nonn

Examples

			a(3)=13 because of the 15 matchings on 3 edges, two do not lie in the D&P Family. In canonical sequence form, the missing matchings are given by 121323 and 123123.
		

Links

• A. Condon, B. Davy, B. Rastegari, S. Zhao and F. Tarrant, RNA pseudoknotted structures, Theoret. Comput. Sci. 320(1), (2004), 35-50.
• R. M. Dirks and N. A. Pierce, A partition function algorithm for nucleic acid secondary structure including pseudoknots, J. Compute. Chem. 24 (2003), 1664-1677.
• Aziza Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, PhD Thesis, University of Florida, 2015.
• C. Saule, M. Régnier, J.-M. Steyaert, and A. Denise, Counting RNA pseudoknotted structures, J. Comput. Biol. 18(10), (2011), 1339-1351.

Programs

Maple

f := RootOf(x^3*_Z^6-x^2*_Z^5+2*x*_Z^3-x*_Z^2-_Z+1);
series(f, x=0, 30);

Formula

G.f. f satisfies x^3f^6-x^2f^5+2xf^3-xf^2-f+1=0.