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%I #14 Aug 06 2018 05:33:23
%S 1,1,1,2,4,10,24,63,177,428,1230,2556,8202,18506,18162,119069
%N Distinct perimeter lengths of polygons with regularly spaced vertices.
%C For n points on a circle there are floor(n/2) distinct line segment lengths. Hence an upper bound for a(n) is the number of compositions of n into floor(n/2) nonnegative parts, which is A127040(n-2). To find a(n), the length of A052558(n-2) paths must be computed. - _T. D. Noe_, Jan 13 2007 [edited by _Petros Hadjicostas_, Jul 19 2018]
%e Consider n=4. Label the points on the circle A,B,C and D. Suppose that AB has unit length. Then a(4)=2 because the two 4-gons are ABCDA and ACBDA, with perimeters 4 and 2+2*sqrt(2), respectively.
%Y Cf. A030077.
%K nonn
%O 1,4
%A Peter H. Borcherds (p.h.borcherds(AT)bham.ac.uk)
%E More terms from _T. D. Noe_, Jan 13 2007
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