A341918 Number of strong triangulations of a fixed hexagon with n interior nodes.

1, 15, 155, 1410, 12165, 102548, 856205, 7128420, 59386655, 495973610, 4156326090, 34965061950, 295326872685, 2504471904060, 21322339850120, 182220932483936, 1562911922345700, 13451387178653575, 116149864521206475, 1006036370555080950, 8739349976276626707, 76128234963921173340

Offset: 1

Author

Andrew Howroyd, Feb 23 2021

Keywords

• nonn
• changed

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500

Crossrefs

Column k=3 of A341856.

Programs

PARI

a(n) = {120*(67*n^2 + 138*n + 68)*(4*n+7)!/((3*n+12)!*(n-1)!)}

Formula

a(n) = 120*(67*n^2 + 138*n + 68)*(4*n+7)!/((3*n+12)!*(n-1)!).

a(n) ~ 335*2^(35/2+8*n)*3^(-23/2-3*n)/(n^(5/2)*sqrt(Pi)). - Stefano Spezia, Aug 25 2025