

A256331


Number of Largest Hairpin Family matchings on n edges.


0



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


REFERENCES

A. Jefferson, The Substitution Decomposition of Matchings and RNA Secondary Structures, Ph. D. Dissertation, Univ. of Florida, Math., 2015.


LINKS

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


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*x2*_Z^2*x2*_Z^2+5*_Z3, 1);
series(f, x=0, 30);


CROSSREFS

Sequence in context: A202474 A256336 A256338 * A292875 A077054 A205580
Adjacent sequences: A256328 A256329 A256330 * A256332 A256333 A256334


KEYWORD

nonn


AUTHOR

Aziza Jefferson, Mar 25 2015


STATUS

approved



