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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
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.
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