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 A330660 Triangle read by rows: T(n,k) is the number of polygons formed by connecting the vertices of a regular {2*n+1}-gon such that they make k turns around the center point. 2
 1, 0, 1, 5, 6, 1, 140, 183, 36, 1, 7479, 9982, 2536, 162, 1, 636944, 880738, 267664, 28381, 672, 1, 79661322, 113973276, 39717471, 5860934, 285078, 2718, 1, 13781863080, 20321795499, 7893750308, 1475570241, 113442968, 2712595, 10908, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Polygons that differ by rotation or reflection are counted separately. By "2*n+1-sided polygons" we mean the polygons that can be drawn by connecting 2*n+1 equally spaced points on a circle. T(0,0)=1 by convention. T(n,k) is the number of polygons with 2*n+1 sides whose winding number around the center point is k. Only polygons with an odd number of sides are considered, since even-sided polygons may have diagonals passing through the center point. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..54 Ludovic Schwob, Illustration of T(3,k), 0 <= k <= 3 Dan Sunday, Inclusion of a Point in a Polygon, (2001). Wikipedia, Winding number FORMULA T(n,n)=1 for all n >= 0: The only solution is the polygon with Schläfli symbol {2n*1/n}. EXAMPLE Triangle begins:      1;      0,    1;      5,    6,    1;    140,  183,   36,   1;   7479, 9982, 2536, 162,  1; PROG (PARI) T(n)={   local(Cache=Map());   my(dir(p, q)=if(p<=n, if(q>n&&q<=p+n, 'x, 1), if(q<=n&&q>=p-n, 1/'x, 1)));   my(recurse(k, p, b) = my(hk=[k, p, b], z); if(!mapisdefined(Cache, hk, &z),   z = if(k==0, 1, sum(q=1, 2*n, if(!bittest(b, q), dir(p, q)*self()(k-1, q, b+(1<

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)