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 A343369 Triangle read by rows: T(n,k) is the number of polygons formed by connecting the vertices of a regular 2n-gon such that the winding number around the center is k and with no side passing through the center. 2
 0, 0, 1, 6, 10, 0, 296, 391, 56, 1, 21580, 28298, 6132, 246, 0, 2317884, 3137098, 859536, 70389, 1012, 1, 349281380, 490054052, 158307216, 19756138, 711692, 4082, 0, 70651004192, 102443715659, 37521267472, 6221752657, 390266848, 6782563, 16368, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Polygons that differ by rotation or reflection are counted separately. T(1,0)=0 by convention. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..55 (rows 1..10) Ludovic Schwob, Illustration of T(4,k), k=0..3 Wikipedia, Winding number FORMULA T(2*n,2*n-1) = 1 and T(2*n+1,2*n) = 0 for all n>=1. T(n,n-2) = 4^(n-1)-2*n for all n>=2. EXAMPLE Triangle begins:       0;       0,     1;       6,    10,    0;     296,   391,   56,   1;   21580, 28298, 6132, 246,   0; PROG (PARI) T(n)={   local(Cache=Map());   my(dir(p, q)=if(p=n&&qp-n, 1/'x, 1)));   my(recurse(k, p, b) = my(hk=[k, p, b], z); if(!mapisdefined(Cache, hk, &z),   z = if(k==0, p<>n, sum(q=1, 2*n-1, if(!bittest(b, q) && (q-p)%n, dir(p, q)*self()(k-1, q, b+(1<

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Last modified September 28 20:00 EDT 2021. Contains 347717 sequences. (Running on oeis4.)