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A256331
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Number of Largest Hairpin Family matchings on n edges.
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0
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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
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1,2
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COMMENTS
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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.
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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..21.
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FORMULA
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G.f. f satisfies x*f^3 - (2*x+2)*f^2 + 5*f - 3 = 0.
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EXAMPLE
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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.
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MAPLE
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f := RootOf(_Z^3*x-2*_Z^2*x-2*_Z^2+5*_Z-3, 1);
series(f, x=0, 30);
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CROSSREFS
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Sequence in context: A202474 A256336 A256338 * A292875 A077054 A205580
Adjacent sequences: A256328 A256329 A256330 * A256332 A256333 A256334
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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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