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A341853
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Number of triangulations of a fixed pentagon with n internal nodes.
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3
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5, 21, 105, 595, 3675, 24150, 166257, 1186680, 8717940, 65572325, 502957455, 3922142574, 31021294850, 248377859100, 2010068042625, 16421073515280, 135277629836412, 1122788441510820, 9381874768828100, 78871575753345375, 666727830129370275
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OFFSET
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0,1
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COMMENTS
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These may be called rooted [n,2] triangulations.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..500
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FORMULA
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a(n) = 210*binomial(4*n+5, n)/((3*n+6)*(3*n+7)).
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EXAMPLE
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The a(0) = 5 triangulations correspond with the dissections of a pentagon by nonintersecting diagonals into 3 triangles. Although there is only one essentially different dissection, each rotation is counted separately here.
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MATHEMATICA
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Array[210 Binomial[4 # + 5, #]/((3 # + 6)*(3 # + 7)) &, 21, 0] (* Michael De Vlieger, Feb 22 2021 *)
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PROG
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(PARI) a(n) = {210*binomial(4*n+5, n)/((3*n+6)*(3*n+7))}
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CROSSREFS
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Column k=2 of A146305.
Sequence in context: A097175 A100284 A337168 * A260845 A325157 A218299
Adjacent sequences: A341850 A341851 A341852 * A341854 A341855 A341856
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KEYWORD
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nonn
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AUTHOR
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Andrew Howroyd, Feb 21 2021
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STATUS
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approved
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