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

2,2

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.

Formula

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

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

Mathematica

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

Crossrefs

Sequence in context: A269532 A269673 A231896 * A072335 A081161 A032106

Adjacent sequences: A128647 A128648 A128649 * A128651 A128652 A128653

Keyword

nonn

Author

Ralf Stephan, May 08 2007

Status

approved