A128650 Number of polygons on n vertices with exactly three faces.

0, 4, 16, 60, 224, 840, 3168, 12012, 45760, 175032, 671840, 2586584, 9984576, 38630800, 149768640, 581690700, 2262890880, 8815845720, 34389986400, 134312002440, 525129633600, 2055166429680, 8050465600320, 31561484455800

Offset: 2

Author

Ralf Stephan, May 08 2007

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..200
• T. Mansour and S. Severini, Grid polygons from permutations and their enumeration by the kernel method, arXiv:math/0603225 [math.CO], 2006.

Programs

Mathematica

Table[4 Binomial[2n-4, n-3], {n, 2, 25}] (* Jean-François Alcover, Dec 05 2018 *)

Formula

a(n) = 4*(n-2)/(n-1) * C(2*n-4,n-2).

For n>2, a(n) = 4*A001791(n-2).