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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
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.
LINKS
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: A346966 A256336 A256338 * A292875 A077054 A355291
KEYWORD
nonn
AUTHOR
Aziza Jefferson, Mar 25 2015
STATUS
approved