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Number of 2*n-sided cycles with the property that one makes the same number of left and right turns while following its edges.
1

%I #8 May 05 2024 08:43:44

%S 4,36,1240,73240,7171176,1016813448,198480110880,50752206180576,

%T 16460660622560680,6595414427636900536,3198428240666246044704,

%U 1845848150787599809368856,1250049326783769438348496480,981653074459964543314138858320

%N Number of 2*n-sided cycles with the property that one makes the same number of left and right turns while following its edges.

%C Cycles that differ by rotation or reflection are counted separately. By "n-sided cycles" we mean the cycles that can be drawn by connecting n equally spaced points on a circle (possibly self-intersecting).

%H Ludovic Schwob, <a href="/A371611/a371611.pdf">Illustration of a(3)</a>

%F a(n) is always divisible by 2*n, because the considered cycles cannot have rotational symmetry.

%Y Cf. A365094, A295264,

%K nonn

%O 2,1

%A _Ludovic Schwob_, Mar 29 2024