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 A341853 Number of triangulations of a fixed pentagon with n internal nodes. 5
 5, 21, 105, 595, 3675, 24150, 166257, 1186680, 8717940, 65572325, 502957455, 3922142574, 31021294850, 248377859100, 2010068042625, 16421073515280, 135277629836412, 1122788441510820, 9381874768828100, 78871575753345375, 666727830129370275 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS These may be called rooted [n,2] triangulations. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 K. A. Penson, K. Górska, A. Horzela, and G. H. E. Duchamp, Hausdorff moment problem for combinatorial numbers of Brown and Tutte: exact solution, arXiv:2209.06574 [math.CO], 2022. FORMULA a(n) = 210*binomial(4*n+5, n)/((3*n+6)*(3*n+7)). EXAMPLE 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. MATHEMATICA Array[210 Binomial[4 # + 5, #]/((3 # + 6)*(3 # + 7)) &, 21, 0] (* Michael De Vlieger, Feb 22 2021 *) PROG (PARI) a(n) = {210*binomial(4*n+5, n)/((3*n+6)*(3*n+7))} CROSSREFS Column k=2 of A146305. Sequence in context: A097175 A100284 A337168 * A260845 A325157 A218299 Adjacent sequences: A341850 A341851 A341852 * A341854 A341855 A341856 KEYWORD nonn AUTHOR Andrew Howroyd, Feb 21 2021 STATUS approved

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Last modified April 19 07:30 EDT 2024. Contains 371782 sequences. (Running on oeis4.)