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A256332
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Number of D&P Family matchings on n edges.
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0
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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
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OFFSET
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1,2
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REFERENCES
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A. Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, Ph. D. Dissertation, Univ. of Florida, Math., 2015.
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LINKS
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Table of n, a(n) for n=1..30.
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.
C. Saule, M. Régnier, J.-M. Steyaert, and A. Denise, Counting RNA pseudoknotted structures, J. Comput. Biol. 18(10), (2011), 1339-1351.
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FORMULA
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G.f. f satisfies x^3f^6-x^2f^5+2xf^3-xf^2-f+1=0.
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EXAMPLE
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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.
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MAPLE
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f := RootOf(x^3*_Z^6-x^2*_Z^5+2*x*_Z^3-x*_Z^2-_Z+1);
series(f, x=0, 30);
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CROSSREFS
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Sequence in context: A284714 A200475 A106227 * A284715 A186577 A141342
Adjacent sequences: A256329 A256330 A256331 * A256333 A256334 A256335
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KEYWORD
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nonn
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AUTHOR
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Aziza Jefferson, Mar 25 2015
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STATUS
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approved
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