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A289031
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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.
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0
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1, 8, 42, 186, 759, 2970, 11369, 43024, 161889, 607630, 2279156, 8552292, 32124073, 120828404, 455175495, 1717506346, 6491412107, 24575174688, 93187097419, 353912403794, 1346146363275, 5127660231072, 19559151930621, 74706450932970
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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