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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 (list; graph; refs; listen; history; text; internal format)
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*x-2*_Z^2*x-2*_Z^2+5*_Z-3, 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

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Last modified April 19 04:19 EDT 2019. Contains 322237 sequences. (Running on oeis4.)