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 A341854 Number of triangulations of a fixed hexagon with n internal nodes. 4
 14, 84, 504, 3192, 21252, 147420, 1057224, 7791168, 58727214, 451137596, 3521923944, 27878644080, 223353322920, 1808402199660, 14778966163752, 121784464712064, 1011022286145816, 8449458780183120, 71042841567457760, 600615322603936920, 5103281457829103220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS These may be called rooted [n,3] 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) = 1008*binomial(4*n+7, n)/((3*n+8)*(3*n+9)). MATHEMATICA Array[1008 Binomial[4 # + 7, #]/((3 # + 8) (3 # + 9)) &, 21, 0] (* Michael De Vlieger, Feb 22 2021 *) PROG (PARI) a(n) = {1008*binomial(4*n+7, n)/((3*n+8)*(3*n+9))} CROSSREFS Column k=3 of A146305. Sequence in context: A027818 A054149 A273182 * A025607 A272103 A244865 Adjacent sequences: A341851 A341852 A341853 * A341855 A341856 A341857 KEYWORD nonn AUTHOR Andrew Howroyd, Feb 21 2021 STATUS approved

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Last modified May 18 02:04 EDT 2024. Contains 372615 sequences. (Running on oeis4.)