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%I #31 Mar 06 2022 10:36:08
%S 1,8,42,186,759,2970,11369,43024,161889,607630,2279156,8552292,
%T 32124073,120828404,455175495,1717506346,6491412107,24575174688,
%U 93187097419,353912403794,1346146363275,5127660231072,19559151930621,74706450932970
%N Number of perfect matchings on n+3 edges which represent RNA secondary folding structures characterized by the Reeder and Giegerich and the Lyngso and Pedersen families, but not the family characterized by Cao and Chen.
%C These matchings can be created inductively by beginning with a hairpin that has a single edge inserted into its middle, then inserting noncrossing matchings into the matching. Finally we can inflate the edges of the hairpin by ladders.
%H Aziza Jefferson <a href="http://ufdc.ufl.edu/UFE0047620">The Substitution Decomposition of Matchings and RNA Secondary Structures</a>, PhD Thesis, University of Florida, 2015.
%F a(n) = 2*a(n-1) - a(n-2) + A003517(n+1).
%F D-finite recurrence: (n-1)*(n+5)*a(n) = 2*(3*n^2 + 9*n - 2)*a(n-1) - (3*n + 1)*(3*n + 7)*a(n-2) + 2*(n+1)*(2*n + 3)*a(n-3). - _Vaclav Kotesovec_, Jun 24 2017
%F a(n) ~ 2^(2*n+8) / (3*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jun 27 2017
%Y Cf. A003517.
%K nonn
%O 1,2
%A _Kyle Goryl_, Jun 22 2017
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