%I
%S 1,0,1,2,1,5,6,1,24,28,8,119,183,57,1,832,1209,432,47,6255,9514,3760,
%T 630,1,54380,82636,36352,7828,244,515284,812714,383648,94997,7756,1,
%U 5454624,8727684,4377888,1243482,153536,1186
%N Irregular triangle read by rows: T(n,k) is the number of n+2sided polygons with the property that one makes k turns on itself while following its edges.
%C Polygons that differ by rotation or reflection are counted separately.
%C By "n+2sided polygons" we mean the polygons that can be drawn by connecting n+2 equally spaced points on a circle (possibly selfintersecting).
%C T(0,0)=1 by convention.
%C To compute the number of turns, follow the edges of the polygon, and add the angles of rotation: positive if turning left, negative if turning right. Then take the absolute value of the sum (see illustration).
%H Ludovic Schwob, <a href="/A342968/a342968.pdf">Illustration of T(5,k), 0 <= k <= 3</a>
%F T(2*n1,n)=1 for all n >= 1: the only solution is the polygon with SchlĂ¤fli symbol {2*n+1/n}.
%e Triangle begins:
%e 1;
%e 0, 1;
%e 2, 1;
%e 5, 6, 1;
%e 24, 28, 8;
%e 119, 183, 57, 1;
%Y Row sums give A001710(n+1) (number of polygons with n+2 sides).
%K nonn,tabf,more
%O 0,4
%A _Ludovic Schwob_, Apr 01 2021
