A344311 - OEIS

%I #32 Sep 12 2021 09:58:49

%S 0,0,0,0,5,18,49,96,198,320,550,708,1235,1582,2415,2912,4284,4518,

%T 7068,8080,11025,12430,16445,16992,23650,26000,32994,35896,44863,

%U 42090,59675,64064,77880,83232,99960,102132,126429,133950,157833,166560,194750,191310,237790,249480,287595,301070

%N Number of polygons formed outside a regular n-gon when every pair of vertices of  the n-gon are joined by an infinite line.

%C See A344857 for other examples and images of the polygons.

%C Only finite polygons are counted. - _N. J. A. Sloane_, Jun 11 2021

%F For odd n, a(n) = (2*n^4 - 15*n^3 + 34*n^2 - 21*n)/24 (see A344857).

%F a(n) = A344857(n) - A007678(n).

%e a(5) = 5 as the five connected vertices of a regular pentagon form five triangles outside the pentagon, along with sixteen polygons on the inside.

%Y Cf. A344857 (total number of polygons), A007678 (number of polygons inside the n-gon), A345025 (total number of polygons and open regions), A344938, A344857, A344866, A146213 (number of vertices).

%K nonn

%O 1,5

%A _Scott R. Shannon_, Jun 01 2021

%E Edited by _N. J. A. Sloane_, Sep 12 2021