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A289031 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. 0
1, 8, 42, 186, 759, 2970, 11369, 43024, 161889, 607630, 2279156, 8552292, 32124073, 120828404, 455175495, 1717506346, 6491412107, 24575174688, 93187097419, 353912403794, 1346146363275, 5127660231072, 19559151930621, 74706450932970 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
LINKS
Aziza Jefferson The Substitution Decomposition of Matchings and RNA Secondary Structures, PhD Thesis, University of Florida, 2015.
FORMULA
a(n) = 2*a(n-1) - a(n-2) + A003517(n+1).
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
a(n) ~ 2^(2*n+8) / (3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 27 2017
CROSSREFS
Cf. A003517.
Sequence in context: A055082 A266940 A212337 * A093381 A097788 A171478
KEYWORD
nonn
AUTHOR
Kyle Goryl, Jun 22 2017
STATUS
approved

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)